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Paul Harrenstein, PhD Student, University of Utrecht, The Netherlands


Towards a Notion of Game-theoretical Consequence


1:00pm, Friday 14 May 2004


Von Neumann and Morgenstern presented game-theory as a branch of mathematics that deals with problems that had nowhere been dealt with before. From a mathematical point of view, the participants in a situation of conflict can be seen as each trying to maximize the same function (the outcome of the game) according to an idiosyncratic principle (their preferences). Moreover, none of the players have control over all variables of the function. The also argued that the usual notion of optimality is no longer available and new solution concepts had to be developed to take its place. Most notably among these game-theoretical solution concepts is still that of a Nash-equilibirum. Logical notions of consequence have frequently been related to game-theoretical solution concepts. The correspondence between a formula being classically valid and the existence of a winning strategy for a player in a related two-person game, has been most prominent in this context. We, however, propose a conservative extension of the classical notion of logical consequence for propositional logic based on a generalization of Nash-equilibrium. We construe propositional variables as decision variables that are possibly in the control of various volitional agents an we pursue the logical consequences of this idea. The game-theoretical concept of consequence that results opens up a line of theoretical research in which logic, game theory and social choice theory interact at the same level.

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