Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame perfect Nash equilibria efficiently. However, such an algorithm can fail to identify optimal equilibria, such as those that maximize social welfare. The reason i...

The success of the alpha-beta algorithm in game-playing has shown its value for problem solving in artiicial intelligence, especially in the domain of two-person zero-sum games with perfect-information. However, there exist diierent algorithms for game-tree search. This paper describes and assesses those proposed alternatives according to how they try to overcome the limitations of alpha-beta. ...

Ultimatum game is an experimental paradigm to study human decision making. There are two players, a proposer and a responder, to split a fixed amount of money. According to the traditional economic theory on ultimatum game, proposer should propose the selfish offers to responder as much as possible to maximize proposer’s own outcomes. However, most evidences had showed that people chose more fa...

This paper studies the core of combined games, obtained by summing two coalitional games. It is shown that the set of balanced transferable utility games can be partitioned into equivalence classes of component games to determine whether the core of the combined game coincides with the sum of the cores of its components. On the other hand, for non-balanced games, the binary relation associating...

This paper addresses the question what is the outcome of multi-agent learning via no-regret algorithms in repeated games? Speci cally, can the outcome of no-regret learning be characterized by traditional game-theoretic solution concepts, such as Nash equilibrium? The conclusion of this study is that no-regret learning is reminiscent of ctitious play: play converges to Nash equilibrium in domin...

Given any $$\alpha \in [0,1]$$ , an $$ -constant-sum game (abbreviated as -CS game) on a finite set of players, N, is function that assigns real number to coalition $$S\subseteq N$$ such the sum worth S and its complementary $$N\backslash S$$ times grand coalition. This class contains constant-sum games Khmelnitskaya (Int J Game Theory 32:223–227, 2003) (for = 1$$ ) threats (Kohlberg Neyman, Ga...

In this paper Boolean games are introduced as a class of two-player zero-sum games along with a number of operations on them. We argue that Boolean games can be interpreted as modelling the information structures of two-person zero-sum games. As such they comprise games of imperfect information. The algebra of Boolean games modulo strategic equivalence is then proven to be isomorphic to the Lin...

We present a simple primal-dual algorithm for computing approximate Nash equilibria in two-person zero-sum sequential games with incomplete information and perfect recall (like Texas Hold’em poker). Our algorithm only performs basic iterations (i.e matvec multiplications, clipping, etc., and no calls to external first-order oracles, no matrix inversions, etc.) and is applicable to a broad class...

A discretized game model of an anti-missile defense scenario is presented. Such an engagement is a pursuit of a "blind" evader, committed to satisfy a terminal constraint. It can be formulated as an incomplete information zero-sum pursuit-evasion game with state constraint. Such a game becomes non trivial if the evader has higher maneuverability than the pursuer. In this case the game admits a ...

In this paper, we consider a two persons zero sum game with imprecise values in payoff matrix. All the imprecise values are assumed to be octagonal fuzzy numbers. An approach for solving problems by using ranking of the fuzzy numbers has been considered to solve the fuzzy game problem. By using ranking to the payoffs we convert the fuzzy valued game problem to crisp valued game problem, which c...