### Citation:

Paper | 337 KB |

### Abstract:

The value is a solution concept for n-person strategic games, developed by Nash, Shapley, and Harsanyi. The value of a game is an a priori evaluation of the economic worth of the position of each player, reflecting the players' strategic possibilities, including their ability to make threats against one another. Applications of the value in economics have been rare, at least in part because the existing definition (for games with more than two players)

consists of an ad hoc scheme that does not easily lend itself to computation.

This paper makes three contributions: We provide an axiomatic foundation for the value; exhibit a simple formula for its computation; and extend the value -- its definition, axiomatic characterization, and computational formula -- to Bayesian games. We then apply the value in simple models of corruption, oligopolistic competition, and information sharing.

We examine a solution concept, called the ``value," for n-person strategic games.

In applications, the value provides an a-priori assessment of the monetary worth of a player's position in a strategic game, comprising not only the player's contribution to the total payoff but also the player's ability to inflict losses on other players. A salient feature is that the value takes account of the costs that ``spoilers" impose on themselves.

Our main result is an axiomatic characterization of the value.

For every subset, S, consider the zero-sum game played between S and its complement, where the players in each of these sets collaborate as a single player, and where the payoff is the difference between the sum of the payoffs to the players in S and the sum of payoffs to the players not in S. We say that S has an effective threat if the minmax value of this game is positive. The first axiom is that if no subset of players has an effective threat then all players are allocated the same amount.

The second axiom is that if the overall payoff to the players in a game is the sum of their payoffs in two unrelated games then the overall value is the sum of the values in these two games.

The remaining axioms are the strategic-game analogs of the classical coalitional-games axioms for the Shapley value: efficiency, symmetry, and null player.

*Last updated on 11/15/2020*