We propose a new and simple adaptive procedure for playing a game: ''regret-matching.'' In this procedure, players may depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past. It is shown that our adaptive procedure guarantees that, with probability one, the empirical distributions of play converge to the set of correlated equilibria of the game.
Let P be a real-valued function defined on the space of cooperative games with transferable utility, satisfying the following condition: In every game, the marginal contributions of all players (according to P) are efficient (i.e., add up to the worth of the grand coalition). It is proved that there exists just one such function P-called thepotentiul-and moreover that the resulting payoff vector coincides with the Shapley value. The potential approach is also shown to yield other characterizations for the Shapley value, in particular, in terms of a new internal consistency property. Further results deal with weighted Shapley values (which emerge from the above consistency) and with the nontransferable utility case (where the egalitarian solutions and the Harsanyi value are obtained).
We propose a new and simple adaptive procedure for playing a game: ''regret-matching.'' In this procedure, players may depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past. It is shown that our adaptive procedure guarantees that, with probability one, the empirical distributions of play converge to the set of correlated equilibria of the game.
These results demonstrate that autologous immunoglobulin idiotype can be formulated into an immunogenic, tumor-specific antigen in humans with B-cell lymphoma, and they provide the background for large-scale trials of active specific immunotherapy of this disease.
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