The Polymatrix Gap Conjecture

This paper proposes a novel way to compare classes of strategic games based on their sets of pure Nash equilibria. This approach is then used to relate the classes of zero-sum games, polymatrix, and k-polymatrix games. This paper concludes with a conjecture that k-polymatrix games form an increasing chain of classes.

Multi-party referential communication in complex strategic games

Verbal communication is an ubiquitous aspect of human interaction occurring in many contexts; however, it is primarily studied in the limited context of two people communicating information. Understanding communication in complex, multi-party interactions is both a scientific challenge for psycholinguistics and an engineering challenge for creating artificial agents who can participate in these richer contexts. We adapted the reference game paradigm to an online 3-player game where players refer to objects in order to coordinate selections based on the available utilities. We ran games with shared or individual payoffs and with or without access to language. Our paradigm can also be used for artificial agents; we trained reinforcement learning-based agents on the same task as a comparison. Our dataset shows the same patterns found in simpler reference games and contains rich language of reference and negotiation.

Two Forms of Responsibility in Strategic Games

The paper studies two forms of responsibility, seeing to it and being blamable, in the setting of strategic games with imperfect information. The paper shows that being blamable is definable through seeing to it, but not the other way around. In addition, it proposes a bimodal logical system that describes the interplay between the seeing to it modality and the individual knowledge modality.

Intelligence in Strategic Games

If an agent, or a coalition of agents, has a strategy, knows that she has a strategy, and knows what the strategy is, then she has a know-how strategy. Several modal logics of coalition power for know-how strategies have been studied before. The contribution of the article is three-fold. First, it proposes a new class of know-how strategies that depend on the intelligence information about the opponents’ actions. Second, it shows that the coalition power modality for the proposed new class of strategies cannot be expressed through the standard know-how modality. Third, it gives a sound and complete logical system that describes the interplay between the coalition power modality with intelligence and the distributed knowledge modality in games with imperfect information.

Cognitive Reflection and Theory of Mind of Go Players

Go is a classical Chinese mind game and a highly popular intellectual pursuit in East Asia. In a survey at two Go tournaments (one of them the largest in Europe), we measured cognitive reflection and decision in strategic games (using the classical “beauty contest” game) (N = 327). We found that Go players in our survey had outstanding average cognitive reflection test (CRT) scores: 2.51 among all participants and 2.80 among players of high master level (dan). This value easily outperforms previous measurements, for example, of undergraduates at top universities. The CRT score was closely related to the playing strength, but not to the frequency of playing. On the other hand, frequent players tended to have higher theory of mind, regardless of their playing strengths. However, self-reported patience was not statistically significantly correlated with Go strength or playing frequency.

Designing Strategic Games with Preestablished Nash Equilibrium through Artificial Inference and Global Learning

This work presents novel results obtained by the application of global optimization techniques to the design of finite, normal form games with mixed strategies. To that end, the Fuzzy ASA global optimization method is applied to several design examples of strategic games, demonstrating its effectiveness in obtaining payoff functions whose corresponding games present a previously established Nash equilibrium. In other words, the game designer becomes able to choose a convenient Nash equilibrium for a generic finite state strategic game and the proposed method computes payoff functions that will realize the desired equilibrium, making it possible for the players to reach the favorable conditions represented by the chosen equilibrium. Considering that game theory is a very useful approach for modeling interactions between competing agents and Nash equilibrium represents a powerful solution concept, it is natural to infer that the proposed method may be very useful for strategists in general. In summary, it is a genuine instance of artificial inference of payoff functions after a process of global machine learning, applied to their numerical components.

Experiments on Communication in Games: Introduction to the Special Issue

Communication is an important topic in the experimental study of strategic behavior, both because of the vital role of communication in variety of strategic games, and because of the insights that can be gained through analyzing communication contents in experiments [...]

Cooperative strategic games

The value is a solution concept for n‐person strategic games, developed by Nash, Shapley, and Harsanyi. The value of a game is an a priori evaluation of the economic worth of the position of each player, reflecting the players' strategic possibilities, including their ability to make threats against one another. Applications of the value in economics have been rare, at least in part because the existing definition (for games with more than two players) consists of an ad hoc scheme that does not easily lend itself to computation. This paper makes three contributions: We provide an axiomatic foundation for the value; exhibit a simple formula for its computation; and extend the value—its definition, axiomatic characterization, and computational formula—to Bayesian games. We then apply the value in simple models of corruption, oligopolistic competition, and information sharing.

Ambiguity and long-run cooperation in strategic games

We study the effects of ambiguity on long-run cooperation in infinitely repeated strategic games. Using a simple parametric model of ambiguity, we study conditions for sustaining cooperative equilibria in the long-run. We apply our framework to the prisoner’s dilemma and duopoly models. We find that (i) ambiguity may affect the game’s structure eventually making the noncooperative equilibrium ex ante preferred; (ii) higher levels of ambiguity make long-run cooperation less likely since it makes punishment schemes less effective; and (iii) large levels of ambiguity may preclude the possibility of mutually beneficial long-run agreements, even when cooperation is beneficial from an ex ante perspective.