Depth of strategic reasoning in games

Orthodox game theory assumes indefinitely recursive reasoning ('I think that you think that I think em leader '), but human decision-makers, who are limited by bounded rationality, cannot handle limitless layers of complexity. Recent research corroborates earlier findings that human players tend to operate at only one or two levels of strategic depth.     

Mutual support in games: Some properties of Berge equilibria

The Berge equilibrium concept formalizes mutual support among players motivated by the altruistic social value orientation in games. We prove some basic results for Berge equilibria and their relations to Nash equilibria, and we provide a straightforward method for finding Berge equilibria in n-player games. We explore some specific examples, and we explain how the Berge equilibrium provides a compelling model of cooperation in social dilemmas. We show that the Berge equilibrium also explains coordination in some common interest games and is partially successful in explaining the payoff dominance phenomenon, and we comment that the theory of team reasoning provides alternative solutions to these problems.     

Ambiguous games: evidence for strategic ambiguity aversion

The problem of ambiguity in games is discussed, and a class of ambiguous games is identified. A total of 195 participants played strategic-form games of various sizes with unidentified co-players. In each case, they first chose between a known-risk game involving a co-player indifferent between strategies and an equivalent ambiguous game involving one of several co-player types, each with a different dominant strategy, and then they chose a strategy for the preferred game. Half the players knew that the ambiguous co-player types were equally likely, and half did not. Half expected the outcomes to be known immediately, and half expected a week's delay. Known-risk games were generally preferred, confirming a significant strategic ambiguity aversion effect. In the delay conditions, players who knew that the ambiguous co-player types were equally likely were significantly less ambiguity averse than those who did not. Decision confidence was significantly higher in 2 × 2 than in larger games.     

Ambiguous games: Evidence for strategic ambiguity aversion

The problem of ambiguity in games is discussed, and a class of ambiguous games is identified. A total of 195 participants played strategic-form games of various sizes with unidentified co-players. In each case, they first chose between a known-risk game involving a co-player indifferent between strategies and an equivalent ambiguous game involving one of several co-player types, each with a different dominant strategy, and then they chose a strategy for the preferred game. Half the players knew that the ambiguous co-player types were equally likely, and half did not. Half expected the outcomes to be known immediately, and half expected a week's delay. Known-risk games were generally preferred, confirming a significant strategic ambiguity aversion effect. In the delay conditions, players who knew that the ambiguous co-player types were equally likely were significantly less ambiguity averse than those who did not. Decision confidence was significantly higher in 2 × 2 than in larger games.     

Interpersonal effects of strategic and spontaneous guilt communication in trust games

A social partner’s emotions communicate important information about their motives and intentions. However, people may discount emotional information that they believe their partner has regulated with the strategic intention of exerting social influence. Across two studies, we investigated interpersonal effects of communicated guilt and perceived strategic regulation in trust games. Results showed that communicated guilt (but not interest) mitigated negative effects of trust violations on interpersonal judgements and behaviour. Further, perceived strategic regulation reduced guilt’s positive effects. These findings suggest that people take emotion-regulation motives into account when responding to emotion communication.     

A dynamic-epistemic hybrid logic for intentions and information changes in strategic games

In this paper I present a dynamic-epistemic hybrid logic for reasoning about information and intention changes in situations of strategic interaction. I provide a complete axiomatization for this logic, and then use it to study intentions-based transformations of decision problems.     

Two paradigms for depth of strategic reasoning in games. Response to Colman

We contrast two approaches to probing the depth of theory-of-mind (ToM) reasoning by adults in matrix game settings: our own and that of Stahl and Wilson.     

Reciprocal trust mediates deep transfer of learning between games of strategic interaction

We studied transfer of learning across two games of strategic interaction. We found that the interpersonal relation between two players during and across two games influence development of reciprocal trust and transfer of learning from one game to another. We show that two types of similarities between the games affect transfer: (1) deep similarities facilitate transfer of an optimal solution across games; (2) surface similarities can either facilitate or hinder transfer depending on whether they lead players toward an optimal or sub-optimal solution in the target game. Learning an optimal solution in a context of interdependence between players is associated with development of reciprocal trust, which in turn mediates transfer of learning across games. The results can be used to inform the design of training exercises to develop strategic interaction skills.     

On the short horizon of spontaneous iterative reasoning in logical puzzles and games

A reasoning strategy is iterative when the initial conclusion suggested by a set of premises is integrated into that set of premises in order to yield additional conclusions. Previous experimental studies on game theory-based strategic games (such as the beauty contest game) observed difficulty in reasoning iteratively, which has been partly attributed to bounded individual rationality. However, this difficulty has also been attributed to problems in adequately representing the beliefs, actions, and goals of other agents involved in the games. In four experiments, we observed similar difficulties in iterative reasoning in a variety of puzzles and games that did not involve social interactions with other agents, where they can only be caused by individual cognitive boundaries. Our findings are consistent with the hypothesis that an intrinsic difficulty in iterative reasoning originates from a tendency not to revise our initial mental representation of a problem in light of the initial conclusions that it implies.     

Inconsistencies in extensive games

In certain finite extensive games with perfect information, Cristina Bicchieri (1989) derives a logical contradiction from the assumptions that players are rational and that they have common knowledge of the theory of the game. She argues that this may account for play outside the Nash equilibrium. She also claims that no inconsistency arises if the players have the minimal beliefs necessary to perform backward induction. We here show that another contradiction can be derived even with minimal beliefs, so there is no paradox of common knowledge specifically. These inconsistencies do not make play outside Nash equilibrium plausible, but rather indicate that the epistemic specification must incorporate a system for belief revision. Whether rationality is common knowledge is not the issue.     

Perceived entitativity,stereotype formation,and the interchangeability of group members

The authors investigated the effects of perceived entitativity of a group on the processing of behavioral information about individual group members and the extent to which such information was transferred to other group members. The results of 3 experiments using a savings-in-relearning paradigm showed that trait inferences about a group member, based on that member's behavior, were stronger for low entitative groups and for collections of individuals. However, the transference of traits from 1 group member to other members of the group was stronger for high entitative groups. These results provide strong evidence that the perception of high entitativity involves the abstraction of a stereotype of the group and the transfer of that stereotype across all group members. Implications for group impression formation and stereotyping are discussed.     

A one-person doxastic characterization of Nash strategies

Within a formal epistemic model for simultaneous-move games, we present the following conditions: (1) belief in the opponents’ rationality (BOR), stating that a player believes that every opponent chooses an optimal strategy, (2) self-referential beliefs (SRB), stating that a player believes that his opponents hold correct beliefs about his own beliefs, (3) projective beliefs (PB), stating that i believes that j’s belief about k’s choice is the same as i’s belief about k’s choice, and (4) conditionally independent beliefs (CIB), stating that a player believes that opponents’ types choose their strategies independently. We show that, if a player satisfies BOR, SRB and CIB, and believes that every opponent satisfies BOR, SRB, PB and CIB, then he will choose a Nash strategy (that is, a strategy that is optimal in some Nash equilibrium). We thus provide a sufficient collection of one-person conditions for Nash strategy choice. We also show that none of these seven conditions can be dropped.     

Rationality in games and institutions

Synthese - Against the orthodox view of the Nash equilibrium as “the embodiment of the idea that economic agents are rational” (Aumann, 1985, p 43), some theorists have proposed...     

On the strategic modulation of the time course of facilitation and inhibition of return

In studies of exogenous attentional orienting, response times for targets at previously cued locations are often longer than those for targets at previously uncued locations. This effect is known widely as inhibition of return (IOR). There has been debate as to whether IOR can be observed in discrimination as well as detection tasks. The experiments reported here confirm that IOR can be observed when target discrimination is required and that the cue-target interval at which IOR is observed is often longer in discrimination than in detection tasks. The results also demonstrate that the later emergence of IOR is related to perceptual discrimination rather than to response selection differences between discrimination and detection tasks. More difficult discrimination tasks lengthen the SOA at which IOR emerges. In contrast, increasing task difficulty by adding a distractor to the location opposite the target shortens the SOA at which IOR emerges. Together, the results reveal an adaptive interaction between exogenous and endogenous attentional systems, in which the action of the orienting (exogenous) system is modulated endogenously in accord with task demands.     

Symptom utilization in strategic therapy

Five techniques of symptom utilization have been presented in an interactional strategic approach. They are: utilization of peers, utilization of the desire to grow up, utilization of personal ambition and future expectations, utilization of an antagonistic relationship, and utilization of sibling rivalry. Emphasis is placed on helping the therapist develop a way of thinking to approach difficult problems.