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A Dynamic-Logical Characterization of Solutions to Sight-limited Extensive Games

Liu C., Liu F., Su K.

Fundamenta Informaticae

2018

Vol. 158, nr 1/3

149--169

An unrealistic assumption in classical extensive game theory is that the complete game tree is fully perceivable by all players. To weaken this assumption, a class of games (called games with short sight) was proposed in literature, modelling the game scenarios where players have only limited foresight of the game tree due to bounded resources and limited computational ability. As a consequence, the notions of equilibria in classical game theory were refined to fit games with short sight. A crucial issue that thus arises is to determine whether a strategy profile is a solution to a game. To study this issue and address the underlying idea and theory on players’ decisions in such games, we adopt a logical way. Specifically, we develop a logic called DLS through which features of these games are demonstrated. More importantly, it enables us to characterize the solutions to these games via formulas of this logic. Moreover, we study the algorithm for model checking DLS, which is shown to be PTIME-complete in the size of the model. This work not only provides an insight into a more realistic model in game theory, but also enriches the possible applications of logic.

A process algebraic form to represent extensive games

Gheibi O., Ramezanian R.

Control and Cybernetics

2015

Vol. 44, no. 1

129--148

In this paper, we introduce an agent-based representation of games, in order to propose a compact representation for multi-party games in game theory. Our method is inspired by concepts in process theory and process algebra. In addition, we introduce an algorithm whose input is a game in the form of process algebra (proposed in this paper) and as an output, the algorithm ﬁnds the Nash equilibrium of the game in linear space complexity.

Game Solution, Epistemic Dynamics and Fixed-Point Logics

van Benthem J., Gheerbrant A.

Fundamenta Informaticae

2010

Vol. 100, nr 1/4

19-41

Current methods for solving games embody a form of "procedural rationality" that invites logical analysis in its own right. This paper is a brief case study of Backward Induction for extensive games, replacing earlier static logical definitions by stepwise dynamic ones. We consider a number of analysis from recent years that look different conceptually, and find that they are all mathematically equivalent. This shows how an abstract logical perspective can bring out basic invariant structure in games. We then generalize this to an exploration of fixed-point logics on finite trees that best fit game-theoretic equilibria. We end with some open questions that suggest a broader program for merging current computational logics with notions and results from game theory. This paper is largely a program for opening up an area: an extended version of the technical results will be found in the forthcoming dissertation [26].