Related papers: On Iterated Dominance, Matrix Elimination, and Mat…

We study the effectiveness of iterated elimination of strictly-dominated actions in random games. We show that dominance solvability of games is vanishingly small as the number of at least one player's actions grows. Furthermore,…

We consider the computational complexity of the question whether a certain strategy can be removed from a game by means of iterated elimination of dominated strategies. In particular, we study the influence of different definitions of…

Dominance is a fundamental concept in game theory. In normal-form games dominated strategies can be identified in polynomial time. As a consequence, iterative removal of dominated strategies can be performed efficiently as a preprocessing…

Recently, in [K.R. Apt and S. Simon: Well-founded extensive games with perfect information, TARK21], we studied well-founded games, a natural extension of finite extensive games with perfect information in which all plays are finite. We…

Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games…

We compare two procedures for the iterated removal of strictly dominated strategies. In the nested procedure, a strategy of a player is removed only if it is dominated by an unremoved strategy. The universal procedure is more comprehensive…

The game theoretic concepts of rationalizability and iterated dominance are closely related and provide characterizations of each other. Indeed, the equivalence between them implies that in a two player finite game, the remaining set of…

In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…

We study the conditions under which the iterated elimination of strictly dominated strategies is order independent and we identify a class of discontinuous games for which order does not matter. In this way, we answer the open problem…

In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of…

The recent discovery of zero-determinant strategies for the iterated Prisoner's Dilemma sparked a surge of interest in the surprising fact that a player can exert unilateral control over iterated interactions. These remarkable strategies,…

We investigate the difficulty of finding economically efficient solutions to coordination problems on graphs. Our work focuses on two forms of coordination problem: pure-coordination games and anti-coordination games. We consider three…

We study the problem of finding Stackelberg equilibria in games with a massive number of players. So far, the only known game instances in which the problem is solved in polynomial time are some particular congestion games. However, a…

We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…

This paper studies how to efficiently update the saddle-point strategy, or security strategy of one player in a matrix game when the other player develops new actions in the game. It is well known that the saddle-point strategy of one…

Iterated regret minimization has been introduced recently by J.Y. Halpern and R. Pass in classical strategic games. For many games of interest, this new solution concept provides solutions that are judged more reasonable than solutions…

The peculiarity of adversarial team games resides in the asymmetric information available to the team members during the play, which makes the equilibrium computation problem hard even with zero-sum payoffs. The algorithms available in the…

The game domination number is a graph invariant that arises from a game, which is related to graph domination in a similar way as the game chromatic number is related to graph coloring. In this paper we show that verifying whether the game…

Adversarial multiplayer games are an important object of study in multiagent learning. In particular, polymatrix zero-sum games are a multiplayer setting where Nash equilibria are known to be efficiently computable. Towards understanding…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…