Games on graphs with a public signal monitoring

We study pure Nash equilibria in games on graphs with an imperfect monitoring based on a public signal. In such games, deviations and players responsible for those deviations can be hard to detect and track. We propose a generic epistemic game abstraction, which conveniently allows to represent the knowledge of the players about these deviations, and give a characterization of Nash equilibria in terms of winning strategies in the abstraction. We then use the abstraction to develop algorithms for some payoff functions.Comment: 28 page

Valuation equilibrium

We introduce a new solution concept for games in extensive form with perfect information, valuation equilibrium, which is based on a partition of each player's moves into similarity classes. A valuation of a player'is a real-valued function on the set of her similarity classes. In this equilibrium each player's strategy is optimal in the sense that at each of her nodes, a player chooses a move that belongs to a class with maximum valuation. The valuation of each player is consistent with the strategy profile in the sense that the valuation of a similarity class is the player's expected payoff, given that the path (induced by the strategy profile) intersects the similarity class. The solution concept is applied to decision problems and multi-player extensive form games. It is contrasted with existing solution concepts. The valuation approach is next applied to stopping games, in which non-terminal moves form a single similarity class, and we note that the behaviors obtained echo some biases observed experimentally. Finally, we tentatively suggest a way of endogenizing the similarity partitions in which moves are categorized according to how well they perform relative to the expected equilibrium value, interpreted as the aspiration level

The Computational Complexity of Single-Player Imperfect-Recall Games

We study single-player extensive-form games with imperfect recall, such as the Sleeping Beauty problem or the Absentminded Driver game. For such games, two natural equilibrium concepts have been proposed as alternative solution concepts to ex-ante optimality. One equilibrium concept uses generalized double halving (GDH) as a belief system and evidential decision theory (EDT), and another one uses generalized thirding (GT) as a belief system and causal decision theory (CDT). Our findings relate those three solution concepts of a game to solution concepts of a polynomial maximization problem: global optima, optimal points with respect to subsets of variables and Karush-Kuhn-Tucker (KKT) points. Based on these correspondences, we are able to settle various complexity-theoretic questions on the computation of such strategies. For ex-ante optimality and (EDT,GDH)-equilibria, we obtain NP-hardness and inapproximability, and for (CDT,GT)-equilibria we obtain CLS-completeness results.Comment: Long version of the paper that got accepted to the Thirty-Second International Joint Conference on Artificial Intelligence (IJCAI-23). 10 pages and 2 figures in the main body. 17 pages and 4 figures in the appendi

Valuation Equilibria

We introduce a new solution concept for games in extensive form with perfect information: the valuation equilibrium. The moves of each player are partitioned into similarity classes. A valuation of the player is a real valued function on the set of her similarity classes. At each node a player chooses a move that belongs to a class with maximum valuation. The valuation of each player is \emph{consistent} with the strategy profile in the sense that the valuation of a similarity class is the player expected payoff given that the path (induced by the strategy profile) intersects the similarity class. The solution concept is applied to decision problems and multi-player extensive form games. It is contrasted with existing solution concepts. An aspiration-based approach is also proposed, in which the similarity partitions are determined endogenously. The corresponding equilibrium is called the aspiration-based valuation equilibrium (ASVE). While the Subgame Perfect Nash Equilibrium is always an ASVE, there are other ASVE in general. But, in zero-sum two-player games without chance moves every player must get her value in any ASVE.bounded rationality, valuation, similarity, aspiration.

Approximating n-player behavioural strategy nash equilibria using coevolution

Coevolutionary algorithms are plagued with a set of problems related to intransitivity that make it questionable what the end product of a coevolutionary run can achieve. With the introduction of solution concepts into coevolution, part of the issue was alleviated, however efficiently representing and achieving game theoretic solution concepts is still not a trivial task. In this paper we propose a coevolutionary algorithm that approximates behavioural strategy Nash equilibria in n-player zero sum games, by exploiting the minimax solution concept. In order to support our case we provide a set of experiments in both games of known and unknown equilibria. In the case of known equilibria, we can confirm our algorithm converges to the known solution, while in the case of unknown equilibria we can see a steady progress towards Nash. Copyright 2011 ACM