2.1 Methods

2.1.2 Tools

Six image-sets were tested, each consisted of several illustrations of a specific object or concept, ranging from its worst to its best condition (such as depictions of trees ranging from a bare tree to a tree with rich and beautiful foliage). Three methods were used to compose these sets. Two image-sets (49 illustrations of cities and 54 illustrations of birds) were compiled using the Google image search engine. Two image-sets (36 trees with leaves and 20 treasure troves) were artistically designed to represent ordinal changes along a bounded continuum (i.e., the number of leaves on an illustrated tree, or the number of valuable objects piled together). The two remaining image-sets (41 jars and 41 sliced trees) were designed to represent fixed intervals along a bounded continuum by systematically decreasing the amount of sand in the depicted jars or systematically slicing the tree images. See Fig. 2 for image-sets examples.

Fig. 2 Reduced image-sets applied as Symbolic Quantification Tools (SQTs). From top to bottom: trees with leaves, treasure troves, jars, and sliced trees. The complete image sets with their corresponding elicited values are available in the supplementary materials

2.2 Results

To test whether the image-sets serve as a reliable and valid tool for transforming non-numeric perceptions into numeric values, we examined the extent to which the same image was identically perceived across participants. To this end, we calculated standard deviations for the ratings of each image across participants. The mean standard deviations of the perceived values, pooled across all images, for the jars, sliced trees, trees with leaves, birds, treasure troves, and cities image-sets were 0.87, 0.94, 1.50, 1.74, 1.91, 2.16, respectively (where the ratings range from 0 to 10). These values suggest rather identical image valance perception across image-sets. Figure 3 depicts means and standard deviations for each of the images in all six image-sets.

Fig. 3 Means and standard deviations for each image in the six image-sets tested in Study 1

While all the image-sets enabled participants to provide clearly differentiated values, we removed the cities image-set because it had the highest mean standard deviation. We also removed the birds image-set due to its relatively large deviation from a linear pattern. All the other sets, namely jars, trees with leaves, sliced trees, and treasure troves, were then used in Study 2, allowing to elicit individual perceptions across eight conflict scenarios.

3.1 Matrices’ strategic resemblance index (MSRI)

The ability of the elicitation procedure to reveal identical SGSs is an essential requirement. While two repeatedly elicited SGSs are not likely to reveal completely identical payoffs, SGSs that describe the same conflict perception of the same person are expected to reflect rather similar properties. To test the reliability of repeatedly elicited SGSs, we defined and tested the MSRI. This index assesses the extent to which two matrices resemble one another, as derived from their strategic properties. The better the fit of the strategic properties of the compared matrices, the higher the MSRI value. The MSRI compares a basic and rather representative set of strategic properties, which represent classical game theory considerations as well as considerations derived from the theory of Subjective Expected Relative Similarity (Fischer, Reference Fischer2009, Reference Fischer2012), further described below. While the selected properties do not exhaust all possible strategic considerations, they do provide a rather broad representation of critical strategic motivations that allows testing how similar or different two matrices are from each other.

The MSRI examines properties that characterize each player separately, properties that involve the interaction of both players, and properties that involve the players themselves—specifically their similarity to each other. The compared properties include: Dominant, Maximin and Maximax strategies; Pareto and Nash equilibria (Luce & Raiffa, Reference Luce and Raiffa1957; Nash, Reference Nash1950); and similarity thresholds as derived from the SERS theory (see Table 1 for property definitions). While these properties are far from exhausting all possible strategic properties, their combination provides a diverse set of characteristics that allows comparing two games and assessing their resemblance. The MSRI value quantifies the extent to which the examined properties point to the choice of the same alternative in both matrices.

Table 1 MSRI property definitions

Dominant strategy	A strategy that provides a better payoff under each and every choice of the opponent
Maximin strategy	A ‘pessimistic’ strategy that considers the minimal payoff under each alternative, and points to the alternative that contains the maximum of these minima, allowing the decision maker to avoid the worst-case scenario
Maximax strategy	An ‘optimistic’ strategy that considers the maximal payoff under each alternative, and points to the alternative that contains the maximum of these maxima, allowing the decision maker to aspire gaining the largest possible payoff
Nash equilibrium	An outcome (cell) that none of the players is motivated to abandon unilaterally, assuming the other player does not change his/her choice
Pareto equilibrium	An outcome (cell) that is optimal in the sense that no other outcome of the game provides higher payoffs for both players
Similarity threshold	A threshold value, computed from the game's payoffs, quantifying the switching point between the two alternatives in relation to the perception of strategic similarity of the opponent. If the perception is above the threshold, the player is expected to choose one of the alternatives; if the perception falls short from the threshold, the player is expected to choose the other alternative. This threshold is an essential component of the SERS theory (see supplementary materials—MSRI calculation and examples)

Since alternatives and payoffs are provided intuitively by the participants, it is important to assure that the compared matrices are correctly aligned before calculating the MSRI score. For example, if comparing two classical Prisoner's Dilemma games (Flood, Reference Flood1958; Rapoport & Chammah, Reference Rapoport and Chammah1965), one must assure that the cooperative alternatives are placed in the same row in both matrices; likewise, one must assure that the cooperative alternatives are placed in the same column in both matrices. When the alternatives are not pre-labeled (e.g., cooperation or defection), it is necessary to ensure that the matrices are correctly aligned.Footnote ¹ In the present study, a group of four additional participants served as independent judges examined the elicited SGSs and aligned them before we calculated the MSRI scores.

To calculate the MSRI scores, we define the following three general scoring principles: (i) if the compared property points to an identical choice in both matrices, the index is incremented by one unit; (ii) likewise, if the compared property does not point to any choice in either matrix, the index is incremented by one unit as well; (iii) if the compared property points to different choices for each of the two matrices, or if it points to a choice in only one of the matrices (and is indifferent regarding the choice in the other matrix), the index is incremented by a value that is proportional to the prospects that the player will make the same choice in both matrices, as detailed in the supplementary materials—MSRI calculation and examples. The overall MSRI, aggregated across all properties, may obtain any value between 0.5 and 10 units.Footnote ²

3.2 Game taxonomies

Rapoport and Guyer's (Reference Rapoport and Guyer1966) taxonomy classifies all strictly ordinal two-by-two games (games in which each player's payoffs are represented as ordinal ranks that are different from each other) into ten categories according to the games’ strategic properties. They further suggest an end-state referred to as the game's natural outcome, which constitutes a theoretical solution to the game: (i) If both players have a dominant alternative, they both choose it, and the resulting outcome constitutes the natural outcome of the game. (ii) If only one player has a dominant alternative, he/she chooses it, while the other player chooses the alternative that maximizes his/her own payoff under the expectation that the dominant alternative is chosen. (iii) If no player has a dominant alternative but there is a single Pareto equilibrium in the game, this cell is the natural outcome. Finally, (iv) if all three conditions are not met, each player will attempt to avoid his worst outcome by choosing in accord with the Maximin decision rule.

Since some SGSs are not expected to be strictly ordered (in other words, some of these games may have at least two identical payoff values for at least one of the players), we expand the taxonomy to also include non-strictly ordinal games. Our revision focuses mainly on expending the definition of the natural outcome to account for games with weak dominance (i.e., having an alternative that provides a better or equal payoff under each and every choice of the opponent), and games with no Maximin preferred choices (see supplementary materials—Rapoport and Guyer's Taxonomy of Two-by-Two Games). Additionally, to focus on the main properties of the expected outcomes, we merge some of the original ten categories and add another category, resulting in the following five game categories: (1) Absolutely Stable games, in which both players can jointly obtain their maximal payoff. Such games are regarded as no-conflict games. In other words, both parties easily and naturally converge on a mutually beneficial solution. (2) Stable/Strongly Stable games, in which one or both players are not satisfied with the natural outcome, yet they are not able to influence the outcome of the game by changing, or threatening to change, their choice. In other words, even though there is no mutually beneficial solution, none of the players is motivated to depart from their initial choices. (3) Non-Stable games, in which one or both players are not satisfied with the natural outcome, yet the player/s are able to influence the game's expected outcome by changing or threatening to change their choice. Interactions modeled by these games may be regarded as intractable conflicts, since every action taken by one of the players can be answered with a counteraction of the other player ad infinitum. (4) Prisoners’ Dilemma (PD)-like games.Footnote ³ In these games neither of the players is satisfied with the natural outcome, yet they are not motivated to change their choice. However, unlike Stable/Strongly Stable games, the natural outcome of PD-like games is a Nash equilibrium but not a Pareto equilibrium (since there exists another cell in which both players obtain higher payoffs). In other words, two rational players that consider only the payoffs (and do not incorporate the properties of the opponent, specifically the strategic similarity of the players) are both expected to obtain a smaller payoff than jointly available for both of them in another cell of the matrix. (5) No Natural Outcome games—in this added category, one or both players have no preferred choice (this can only occur in some games that are non-strictly ordinal). Therefore, there is no predicted choice for one or both of the players and consequently no expected outcome. See Fig. 4 for example matrices, and supplementary materials—Rapoport and Guyer's Taxonomy of Two-by-Two Games for a detailed description of the revised taxonomy.

Fig. 4 Example matrices for the five categories of the revised and reduced Rapoport and Guyer taxonomy. In all matrices, except the No Natural Outcome games, the natural outcome is the top left cell. The top Absolutely Stable game is typically referred to as the Stag Hunt game (Skyrms, Reference Skyrms2001). The top Non-Stable game is a Chicken game (Rapoport & Chammah, Reference Rapoport and Chammah1966). The bottom Non-Stable game is typically referred to as Battle of the Sexes (Rapoport, Reference Rapoport1967). The top PD-like game is a classic PD (Flood, Reference Flood1958; Rapoport & Chammah, Reference Rapoport and Chammah1965). The top No Natural Outcome game is a Matching Pennies game (Budescu & Rapoport, Reference Budescu and Rapoport1994)

We also supplement Rapoport and Guyer's (Reference Rapoport and Guyer1966) taxonomy with a taxonomy that is based on the SERS theory (Fischer, Reference Fischer2009, Reference Fischer2012; Fischer & Savranevski, Reference Fischer and Savranevski2023; Fischer et al., Reference Fischer, Levin, Rubenstein, Avrashi, Givon and Oz2022a, Reference Fischer, Rubenstein and Levin2022b), which shifts the focus from the payoff structure per se to the interaction between the game's payoff structure and the players’ perceptions of their opponent; specifically, the prospects of both players to choose identical alternatives. SERS computes an expected value that integrates (i) the perception of strategic similarity, which indicates the probability the opponent will choose an alternative identical to the alternative selected by oneself, and (ii) the payoffs expected under each choice. For example, consider two players choosing their alternatives while interacting in a PD game (Fig. 1). A player who assumes his opponent is sufficiently strategically similar to himself may expect that if he chooses to cooperate the opponent is likely to cooperate as well. But, if the player chooses to defect, he may assume that the opponent is likely to defect as well. In contrast, a player who assumes his opponent is strategically dissimilar to himself may expect that if he chooses to cooperate the opponent is likely to defect. But, if the player chooses to defect, he may assume that the opponent is likely to cooperate. Therefore, a player who perceives the opponent as sufficiently similar is likely to cooperate, while a player who perceives the opponent as dissimilar is likely to defect. Notice that since the perception of strategic similarity is continuous (and not dichotomous—totally similar or totally dissimilar), SERS computes the optimal switching point between alternatives. As shown by previous research, SERS provides both a normative and a descriptive account of human behavior. Games in which the SERS-based expected choices vary under different perceptions of strategic similarity with the opponent are referred to as similarity-sensitive games. Games in which the SERS-based expected choices do not vary under different perceptions of strategic similarity with the opponent are referred to as non-similarity-sensitive games. Clearly, some games can be similarity-sensitive for one of the players and non-similarity-sensitive for the other. Therefore, the similarity-based taxonomy differentiates between two-player similarity-sensitive games, one-player similarity-sensitive games, and two-player non-similarity-sensitive games. The importance of this classification for analysis of the SGSs lies in its capacity to determine which games are susceptible to social and behavioral interventions. That is, influencing perceptions of strategic similarity between the interacting parties has the potential to alter the expected outcome of similarity-sensitive games without changing the game's actual payoffs. See supplementary materials—Similarity-Based Taxonomy of Games for a detailed description of SERS and the respective classification of games.

3.3 Methods

3.3.2 Tools

3.3.2.1 Interaction scenarios

Eight short vignettes, each involving two opposing parties, describing various bilateral interactions. To generate these scenarios while avoiding addressing any actual ongoing conflicts, five research group members individually composed short vignettes describing fictitious geopolitical conflicts that also involve ideological, socio-economic, and terrorism-related aspects. The proposed scenarios were then jointly discussed and revised by all members until a consensus was reached. Five of the eight selected scenarios represent intersections of geopolitical and the other three aspects; two scenarios represent intersections only between the other aspects; and one scenario addresses a purely geopolitical conflict (Fig. 5). The following descriptions are abridged versions of the eight scenarios used in the study (See supplementary materials – Conflict Descriptions for the complete conflict descriptions).

The Caradian—Tiberian Conflict (geopolitical): Two ethnic groups involved in an armed territorial conflict, in which one party (the Caradian people) is militarily superior to the other party (the Tiberian people). The scenario suggests two options, one cooperative and the other confrontational.

The Mireen—Bagotan Conflict (geopolitical ∩ socio-economic): Two countries possess two different natural resources. Yet to benefit from its resource, each country must collaborate with the other country. The scenario suggests two alternatives: signing or rejecting a trade agreement.

The Choppo—Kaipeng Conflict (geopolitical ∩ socio-economic): Two countries struggle with different domestic problems; whose solution is dependent upon the resources of the neighboring country. The scenario suggests a collaborative or a confrontational alternative.

The Taizei—Comoro Conflict (geopolitical ∩ terrorism): A stateless ethnic group struggles for independence, while a powerful country perceives the aspirations of this group as a threat. The scenario suggests attacking or practicing restraint.

The Burgia—Sani Conflict (geopolitical ∩ terrorism): A sovereign country and an indigenous ethnic group claim ownership over the same territory. The sovereign country is more powerful, whereas the ethnic group is weaker and less organized. The scenario suggests a peaceful or an aggressive alternative.

The Maasai—Samburu Conflict (geopolitical ∩ ideological): Two tribes fight over the same territory. The scenario suggests two alternatives for each tribe: to stop, or to carry on fighting.

The Kibbutz Conflict (ideological ∩ socio-economic): A socialist community (kibbutz) is torn apart by two ideologies, each representing a different view on capital ownership. A referendum will determine the community's ideological and economic future.

The Cartel Conflict (socio-economic ∩ terrorism): A country is populated by both high and low socioeconomic-status groups. The low-status group supports the activity of a drug cartel, while the high-status group supports the government. Both sides must consider whether to increase or decrease hostile activities toward the other party.

Fig. 5 The eight conflict scenarios applied in study 2 depicted according to four conflict aspects

3.3.2.2 Symbolic quantification tools (SQT)

After testing and selecting four SQTs in Study 1 (jars, trees with leaves, sliced trees, and treasure troves), we apply these SQTs in Study 2. Participants assigned to the Caradian-Tiberian, Mireen-Bagotan, Burgia-Sani and Kibbutz conflict scenarios responded by using the jars and the trees with leaves SQTs. Participants assigned to the Maasai-Samburu, Choppo-Kaipeng, Taizei-Comoro and the Cartel conflict scenarios responded by using the sliced trees and treasure troves SQTs.

3.3.3 Procedure

Participants were randomly assigned to one of four conditions. Each condition consisted of two specific conflict descriptions and two designated SQTs. All participants went through the following stages: (i) reading a conflict description while being assigned a specific side in the conflict; (ii) describing two possible and different courses of action that could be implemented by the participant's assigned group and by the opponents, yielding four distinct outcomes; (iii) describing a set of five possible consequences that each of the parties will experience under each of the four outcomes; (iv) using two SQTs to rate the consequences associated with each outcome by selecting the illustration that most accurately represents their attitudes towards the consequences provided in the previous stage. This process was implemented first in reference to the participant's assigned party and second in reference to the other party. Participants then repeated all four stages for the second conflict description.

The second session of the study took place about a week after the first. Participants followed the same procedure, with the same conflict descriptions and SQTs presented in reverse order. Finally, participants completed a basic demographic questionnaire and were compensated for their participation in both sessions.

Preparing the data for analysis entailed transforming the conflict alternatives (Stage ii) and the perceptions of the payoffs (Stage iv) into two-by-two game matrices (i.e., SGSs), in which the actions provided for the two sides formed the alternatives for the row and column players. Using the average ratings obtained in Study 1 enabled us to transform the selected SQT images into numeric values that represent expected payoffs. These payoff values were placed in their corresponding cells, generating two-by-two SGSs with action alternatives and expected payoffs (see Fig. 6).

Fig. 6 Illustration of basic SGS elicitation, transformation, and classification processes

3.4 Results

Since the order of action alternatives was provided within each session by the participants, the within-session alternatives are aligned to each other by default. However, the alternatives provided in the two separate sessions are not necessarily reported in the same order. Therefore, these between-session alternatives must be aligned before computing the reliability index—the MSRI. To this end, we recruited four additional participants to serve as independent judges who separately determined whether the alternatives were described in the same order or whether they needed to be aligned. If alignment was necessary, the order of the alternatives in the second session was switched to match their order in the first session. The judges’ alignment recommendations were implemented if at least three of the independent judges reached identical conclusions. If no agreement was reached (two judges recommended switching the order of the alternatives while the other two judges did not recommend switching), the examined matrices were excluded from the between-session MSRI analysis. Overall, the judges reached a high level of agreement, assuring alignment of 91% of between-session SGS pairs. The remaining SGSs, comprising non-alignable matrix pairs and single-session data obtained from participants who did not show up for the second session, were included only in the within-session MSRI analysis.

The following analyses examine three main aspects of the generated SGSs. First, we test the consistency of participants’ conflict perceptions by computing the MSRI values for within-session (between two different SQTs) and between-session (for the same SQT) SGSs. Second, we describe and analyze the distribution of generated SGSs according to the revised Rapaport and Guyer (1966) taxonomy of two-by-two games. Finally, we describe and analyze the distribution of generated game structures according to the similarity-based taxonomy, as derived from the SERS theory (Fischer, Reference Fischer2012; Fischer et al., Reference Fischer, Levin, Rubenstein, Avrashi, Givon and Oz2022a, Reference Fischer, Rubenstein and Levin2022b).

3.4.1 Consistency of participants’ conflict perceptions

For each of the eight conflicts we calculated the MSRI scores for the within-session SGSs (comparing the results obtained from two different SQTs) and the between-sessions SGSs (comparing the results obtained from the same SQT in both sessions). We then compared these values with the MSRI values derived from a set of randomly generated matrix pairs. Comparing two sets of randomly generated two-by-two matrices, obtained under the same constraints on the range of values, is still likely to result in some resemblance of the matrix properties. Hence, the reliability of random matrix pairs serves as a benchmark, or a chance-level value, indicating the lack of genuine behavioral reliability. To evaluate the extent of the reliability observed in the elicited SGSs, we applied a Monte Carlo approach and compared the MSRI values of the SGSs with those of the randomly generated matrices. The larger the difference between MSRI values of behaviorally elicited SGSs and MSRI values of randomly generated matrix pairs, the better the consistency of participants’ conflict perceptions and the higher the reliability. To this end, we generated 30 matrix sets with random payoffs for each scenario. Each set consisted of the same number of matrix pairs as the number of the elicited matrix pairs. We then ran 30 separate t-tests for independent samples to compare participants’ MSRIs with the randomly generated matrices’ MSRIs. Pooling the t-test statistics yielded average t values, $\overline{t}$ , (and their associated p values) and average Cohen's d values, $\overline{d}$ .

Table 2 shows within- and between-session MSRIs and their comparison with the randomly generated sets for all eight conflict scenarios. Within-session MSRI analyses reveal relatively high reliability, ranging from 8.60 (out of a maximum of 10) for the Maasai-Samburu scenario to 9.28 for the Mireen-Bagotan scenario. All comparisons with the randomly generated matrix pairs MSRIs reveal significant differences (p < 0.001, average Cohen's $\overline{d}$ = 2.23). Between-session MSRI analyses reveal a varied pattern of SGS test–retest reliability. The Caradian-Tiberian, Mireen-Bagotan, Burgia-Sani and Choppo-Kaipeng scenarios exhibit high average MSRI values, ranging from 7.30 (Choppo-Kaipeng) to 8.37 (Mireen-Bagotan) across the two SQTs, showing high consistency in the perceptions of these conflicts. The other four scenarios yielded lower between-session reliability, showing low to medium consistency, with the Kibbutz and Cartel scenarios showing the lowest MSRI means (5.34 and 5.24, respectively). These differences are supported by a two-way ANOVA (8 conflicts $\times$ 4 SQTs), revealing significant differences between the eight conflicts (F_(7,416) = 16.25, p < 0.001, η² = 0.21). As expected for equivalent measures, no significant differences between the four SQTs were found (F_(2,416) = 1.28, n.s., η² = 0.006), as well as no significant conflict $\times$ SQT interaction (F_(6,416) = 0.38, n.s., η² = 0.005). Overall, these results suggest that the four SQTs generate equivalent SGSs for the examined scenarios, as shown by the high levels of within-session MSRI values (as compared to the randomly generated sets). Nevertheless, the resulting between-session reliability suggests a difference emanating from the properties of the conflict scenarios themselves. Some scenarios are characterized by high test–retest reliability, meaning that participants’ perceptions of these scenarios are stable over time, whereas other scenarios are characterized by lower test–retest reliability, suggesting that the described scenarios may be perceived in different ways.

Table 2 Study 2 MSRI scores

Scenario	Overall number of participants, dual session participants, align-able matrix pairs	SQT types	Within-session MSRI			Between-session MSRI—SQT 1			Between-session MSRI—SQT 2			Between session mean
			Mean (sd)	Random mean (sd)	t test	Mean (sd)	Random mean (sd)	t test	Mean (sd)	Random mean (sd)	t test
Caradian—Tiberian	37, 27, 26	(1) Jars, (2) Trees with Leaves	8.64 (1.73)	5.33 (1.65)	$\overline{t}$ (63) = 11.08, p < .001, $\overline{d}$ = 1.96	7.49 (2.08)	5.37 (1.76)	$\overline{t}$ (25) = 4.44, p < .001, $\overline{d}$ = 1.15	7.45 (1.79)	5.39 (1.77)	$\overline{t}$ (25) = 4.37, p < .001, $\overline{d}$ = 1.16	7.47
Mireen—Bagotan	37, 27, 25	(1) Jars, (2) Trees with Leaves	9.28 (1.06)	5.33 (1.64)	$\overline{t}$ (63) = 16.24, p < .001, $\overline{d}$ = 2.87	8.36 (1.65)	5.40 (1.67)	$\overline{t}$ (24) = 6.62, p < .001, $\overline{d}$ = 1.79	8.37 (1.56)	5.39 (1.76)	$\overline{t}$ (24) = 6.67, p < .001, $\overline{d}$ = 1.79	8.37
Burgia—Sani	34, 32, 28	(1) Jars, (2) Trees with Leaves	9.09 (1.18)	5.27 (1.67)	$\overline{t}$ (65) = 15.18, p < .001, $\overline{d}$ = 2.64	7.67 (2.09)	5.43 (1.58)	$\overline{t}$ (27) = 4.57, p < .001, $\overline{d}$ = 1.22	7.18 (2.17)	5.50 (1.83)	$\overline{t}$ (27) = 3.17, p = .01, $\overline{d}$ = .84	7.43
Kibbutz	34, 32, 25	(1) Jars, (2) Trees with Leaves	8.73 (1.63)	5.33 (1.72)	$\overline{t}$ (65) = 11.62, p < .001, $\overline{d}$ = 2.02	5.84 (2.35)	5.40 (1.77)	$\overline{t}$ (24) = .77, n.s., $\overline{d}$ = .23	4.84 (2.46)	5.27 (1.72)	$\overline{t}$ (24) = −.72, n.s., $\overline{d}$ = −.20	5.34
Maasai—Samburu	35, 33, 28	(1) Sliced Trees, (2) Treasure Rooms	8.60 (1.91)	5.36 (1.66)	$\overline{t}$ (67) = 10.53, p < .001, $\overline{d}$ = 1.81	6.72 (2.04)	5.49 (1.74)	$\overline{t}$ (27) = 2.47, p = .043, $\overline{d}$ = .65	6.74 (1.91)	5.37 (1.76)	$\overline{t}$ (27) = 2.83, p = .018, $\overline{d}$ = .75	6.73
Choppo—Kaipeng	35, 33, 29	(1) Sliced Trees, (2) Treasure Rooms	8.82 (1.32)	5.31 (1.60)	$\overline{t}$ (67) = 9.22, p < .001, $\overline{d}$ = 2.22	7.22 (2.23)	5.30 (1.75)	$\overline{t}$ (28) = 3.70, p = .001, $\overline{d}$ = .96	7.37 (1.78)	5.37 (1.715)	$\overline{t}$ (28) = 4.44, p = .002, $\overline{d}$ = 1.15	7.30
Taizei—Comoro	33, 32, 27	(1) Sliced Trees, (2) Treasure Rooms	8.67 (1.45)	5.33 (1.69)	$\overline{t}$ (64) = 12.13, p < .001, $\overline{d}$ = 2.13	5.67 (2.38)	5.46 (1.70)	$\overline{t}$ (26) = .39, n.s., $\overline{d}$ = .11	6.08 (1.83)	5.30 (1.69)	$\overline{t}$ (26) = 1.66, n.s., $\overline{d}$ = .45	5.88
Cartel	33, 32, 28	(1) Sliced Trees, (2) Treasure Rooms	8.72 (1.47)	5.28 (1.68)	$\overline{t}$ (64) = 12.47, p < .001, $\overline{d}$ = 2.19	5.07 (2.02)	5.30 (1.78)	$\overline{t}$ (27) = −.46, n.s., $\overline{d}$ = −.12	5.40 (1.87)	5.36 (1.78)	$\overline{t}$ (27) = .07, n.s., $\overline{d}$ = .02	5.24

Within- and between-session Matrix Strategic Resemblance Indices (MSRIs) across eight scenarios, and four Symbolic Quantification Tools (SQTs). Mean MSRI values express behavioral consistency, while random means serve as a reference point for chance-level MSRI values. The t tests compare the elicited MSRI means with the random means

3.4.2 SGS distributions

After establishing relatively high MSRI levels for most of the conflicts, we examine the embedded properties of the elicited SGSs in accordance with two game taxonomies. This stage reveals the previously hidden characteristics of the SGSs, providing meaningful insights that inform decision makers what can and what cannot be attained in each conflict scenario. It also indicates when intervention may be fruitful and help attain cooperative solutions. We first consider the revised Rapoport and Guyer taxonomy of two-by-two games, followed by the similarity-based classification. Together these two perspectives point to both strategic and behavioral properties of the elicited SGSs.

Figure 7 depicts the distribution of game types in accordance with the revised Rapoport and Guyer taxonomy for each of the eight conflicts. All conflicts are characterized by a high proportion of absolutely stable games (ranging from 42% of SGSs for the Taizei-Comoro scenario to 84% of SGSs for the Mireen-Bagotan scenario), followed by a lower proportion of non-stable games (ranging from 12% of SGSs for the Mireen-Bagotan scenario to 36% of SGSs for the Taizei-Comoro scenario). The depicted distributions show that four of the scenarios (Caradian-Tiberian, Mireen-Bagotan, Burgia-Sani and Choppo-Kaipeng) are characterized by a rather similar distribution of game types. These scenarios exhibit a high proportion, about 75%, of absolutely stable games. The other four scenarios are characterized by a more uniform distribution, albeit absolutely stable games remain the most frequent game type. Two of these (Cartel and Taizei-Comoro) show a rather low proportion, about 40%, of absolutely stable games, and the two others (Kibbutz and Maasai-Samburu) reveal a higher proportion of about 55% absolutely stable games. Note that scenarios with high proportions of absolutely stable games are also those that are characterized by high between-session MSRI means.

Fig. 7 Distribution of game types in accordance with the revised Rapoport and Guyer taxonomy, for each of the eight scenarios in Study 2

Figure 8 depicts the distribution of game types in accordance with the similarity-based taxonomy for each of the eight scenarios. For six scenarios, the category of one-player similarity-sensitive games is the most frequent, ranging from 38% for the Kibbutz conflict to 57% for the Taizei-Comoro scenario. For the other two scenarios, Choppo-Kaipeng and Maasai-Samburu, the most frequent category is the two-player similarity-sensitive game, representing 44% and 46%, respectively. Overall, 54% of the players experience the described scenarios as a similarity-sensitive game (summing the percentage of two-player similarity-sensitive games and half of the percentage of one-player similarity-sensitive games). The percentage of these players ranges from 45% for the Kibbutz scenario to 67% for the Maasai-Samburu scenario. This is an important outcome from the perspective of conflict management, since it points to the possibility of applying similarity inducing interventions, which are expected to promote cooperative solutions.

Fig. 8 Distribution of game types in accordance with the similarity-based taxonomy, for each of the eight scenarios in Study 2