We introduce a new mathematical representation of an extensive game situation,called an information protocol, without using the hypothetical underlying structureof nodes and branches. Its necessity has been emerging in our study of inductivegame theory. It has two main differences from a standard extensive game: one is theuse of information pieces (symbolic expressions) rather than information sets, andthe other is the replacement of a game tree by a causal relation. We will give a set ofaxioms to show that our new formulation is equivalent to an extensive game. Also,by deleting some axioms, we can capture some weaker forms of extensive games,which are crucial to describing inductive game theory. Some theoretical resultsfor inductive game theory become drastically simplified in the present formulationrelative to previous formulations by the authors relying on extensive games.
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