A cryptographic solution to a game theoretic problem

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A cryptographic solution to a game theoretic problem (2000)

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by Yevgeniy Dodis , Shai Halevi , Tal Rabin

Venue:	In CRYPTO 2000: 20th International Cryptology Conference
Citations:	73 - 1 self

BibTeX

@INPROCEEDINGS{Dodis00acryptographic,
    author = {Yevgeniy Dodis and Shai Halevi and Tal Rabin},
    title = {A cryptographic solution to a game theoretic problem},
    booktitle = {In CRYPTO 2000: 20th International Cryptology Conference},
    year = {2000},
    pages = {112--130},
    publisher = {Springer}
}

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Abstract

Abstract. In this work we use cryptography to solve a game-theoretic problem which arises naturally in the area of two party strategic games. The standard game-theoretic solution concept for such games is that of an equilibrium, which is a pair of “self-enforcing ” strategies making each player’s strategy an optimal response to the other player’s strategy. It is known that for many games the expected equilibrium payoffs can be much higher when a trusted third party (a “mediator”) assists the players in choosing their moves (correlated equilibria), than when each player has to choose its move on its own (Nash equilibria). It is natural to ask whether there exists a mechanism that eliminates the need for the mediator yet allows the players to maintain the high payoffs offered by mediator-assisted strategies. We answer this question affirmatively provided the players are computationally bounded and can have free communication (so-called “cheap talk”) prior to playing the game. The main building block of our solution is an efficient cryptographic protocol to the following Correlated Element Selection problem, which is of independent interest. Both Alice and Bob know a list of pairs (a1, b1)... (an, bn) (possibly with repetitions), and they want to pick a random index i such that Alice learns only ai and Bob learns only bi. Our solution to this problem has constant number of rounds, negligible error probability, and uses only very simple zero-knowledge proofs. We then show how to incorporate our cryptographic protocol back into a game-theoretic setting, which highlights some interesting parallels between cryptographic protocols and extensive form games. 1

Keyphrases

game theoretic problem cryptographic solution cryptographic protocol player strategy constant number independent interest expected equilibrium payoff game-theoretic problem free communication so-called cheap talk main building block self-enforcing strategy mediator-assisted strategy high payoff optimal response trusted third party game-theoretic setting correlated equilibrium negligible error probability many game correlated element selection problem random index simple zero-knowledge proof interesting parallel extensive form game standard game-theoretic solution concept party strategic game efficient cryptographic protocol

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