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IEEE Transactions on Automatic Control

An example of interaction between information and control: The Transparency of a game

Jean‐Michel Bismut

Published Oct 1, 1973• 40 citations
Publisher

Abstract

This paper presents an example of a two-person cooperative game, where the control of the first player is at the same time information to the second player. It is proved that, under mild assumptions, the information constraint is transparent, i.e., the players behave as if both had been given the same information by means of a coding system. The consequences of this result are examined for noncooperative games. Finally similar results are obtained for multistep games.

DOI
10.1109/tac.1973.1100388

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This paper presents an example of a two-person cooperative game, where the control of the first player is at the same time information to the second player. It is proved that, under mild assumptions, the information constraint is transparent, i.e., the players behave as if both had been given the same information by means of a coding system. The consequences of this result are examined for noncooperative games. Finally similar results are obtained for multistep games.
In a game each player holds a strategy based upon the actions that he can actually take. The quality and the quantity of the feasible actions are determined by his ability or power in the game. Generally every player has no information on the others' powers, so it is one of the most important problems for them to know the powers. We treat such unknown games, played periodically, from the view point of information theory. We discuss both non-cooperative and cooperative games and prove some sufficient conditions under which a player can get the full information on the other players' powers from sequential observations on the states. In two person games we show also optimal strategies with respect to the information.
This paper investigates various aspects of the nonlocal effects that can arise when entangled quantum information is shared between two parties. A natural framework for studying nonlocality is that of cooperative games with incomplete information, where two cooperating players may share entanglement. Here nonlocality can be quantified in terms of the values of such games. We review some examples of nonlocality and show that it can profoundly affect the soundness of two-prover interactive proof systems. We then establish limits on nonlocal behavior by upper-bounding the values of several of these games. These upper bounds can be regarded as generalizations of the so-called Tsirelson inequality. We also investigate the amount of entanglement required by optimal and nearly optimal quantum strategies. 1.
Complementarity games are explorative games between two players. The deterministic rules of the game are known to both players. The first player freely chooses among a finite number of states of the game but tells nobody of this decision. The second player accesses the game only by primitive, symbolic input‐output interfaces. The task of the second player is to find out the unknown state by input‐output experiments. The logic resulting from this scenario resembles‐ quantum logic in many aspects. It is the empirical logic of choice for virtual realities.
This paper investigates various aspects of the nonlocal effects that can arise when entangled quantum information is shared between two parties. A natural framework for studying nonlocality is that of cooperative games with incomplete information, where two cooperating players may share entanglement. Here, nonlocality can be quantified in terms of the values of such games. We review some examples of non-locality and show that it can profoundly affect the soundness of two-prover interactive proof systems. We then establish limits on nonlocal behavior by upper-bounding the values of several of these games. These upper bounds can be regarded as generalizations of the so-called Tsirelson inequality. We also investigate the amount of entanglement required by optimal and nearly optimal quantum strategies.