Cooperation in Games and Epistemic Readings of Independence-Friendly Sentences

Abstract

In the literature on logics of imperfect information it is often stated, incorrectly, that the Game-Theoretical Semantics of Independence-Friendly (IF) quantifiers captures the idea that the players of semantical games are forced to make some moves without knowledge of the moves of other players. We survey here the alternative semantics for IF logic that have been suggested in order to enforce this "epistemic reading" of sentences. We introduce some new proposals, and a more general logical language which distinguishes between "independence from actions" and "independence from strategies". New semantics for IF logic can be obtained by choosing embeddings of the set of IF sentences into this larger language. We compare all the semantics proposed and their purported game-theoretical justifications, and disprove a few claims that have been made in the literature.

Rational coordination with no communication or conventions

“…Clearly, if players can communicate when playing a pure coordination game with at least one winning outcome, then they can simply agree on a winning strategy profile, so the game is trivialised. What makes such games non-trivial is limited (or non-existing) possibility of preplay communication amongst the players 1 , meaning that the players must make their choices based on individual reasoning-without any contact with the other players before (or during) playing the game.…”

“…Furthermore, we note the close conceptual relationship of the present study with the notion of rationalisability of strategies [3], [22], [7], which is particularly important in epistemic game theory. We also mention two recent relevant works-related to logic-to which the observations and results in the present paper could be directly applied: in [14], two-player coordination games are related to a variant of Coalition Logic 4 , and in [1], coordination scenarios are analysed with respect to the game-theoretic semantics of Independence Friendly Logic. Finally, the study on structural conventions with respect to 'random game graphs' in [19] adopts the definitions that were originally conceived in the work leading to the current paper.…”

Rational Coordination with no Communication or Conventions

“…We note the close conceptual relationship of the present study with the notion of rationalisability of strategies [2], [5], [15], which is particularly important in epistemic game theory. We also mention two recent relevant works related to logic to which the observations and results in the present paper could be directly applied: in [10], two-player coordination games were related to a variant of Coalition Logic 3 , and in [1], coordination was analysed with respect to the game-theoretic semantics of Independence Friendly Logic.…”