Fictitious play and- no-cycling conditions

We investigate the paths of pure strategy profiles induced by the fictitious play process. We present rules that such paths must follow. Using these rules we prove that every non-degenerate 2*3 game has the continuous fictitious play property, that is, every continuous fictitious play process, independent of initial actions and beliefs, approaches equilibrium in such games.

The least core, kernel, and bargaining sets of large games

We study the least core, the kernel, and bargaining sets of coalitional games with a countable set of players. We show that the least core of a continuous superadditive game with a countable set of players is a non-empty (norm-compact) subset of the space of all countable additive measures. Then we show that in such games the intersection of the prekernel and least core is non-empty. Finally, we show that this intersection is contained in the Aumann-Maschler and the Mas-Colell bargaining sets

The least core, kernel and bargaining sets of large games

We study the least core, the kernel and bargaining sets of coalitional games with a countable set of players. We show that the least core of a continuous superadditive game with a countable set of players is a non-empty (norm-compact) subset of the space of all countably additive measures. Then we show that in such games the intersection of the prekernel and the least core is non-empty. Finally, we show that the Aumann-Maschler and the Mas-Colell bargaining sets contain the set of all countably additive payoff measures in the prekernel.Publicad

Fictitious play and no-cycling conditions

We investigate the paths of pure strategy profiles induced by the fictitious play process. We present rules that such paths must follow. Using these rules we prove that every non-degenerate 2x3 game has the continuous fictitious play property, that is, every continuous fictitious play process, independent of initial actions and beliefs, approaches equilibrium in such games

Core equivalence theorems for infinite convex games

We show that the core of a continuous convex game on a measurable space of players is a von Neumann-Morgenstern stable set. We also extend the definition of the Mas-Colell bargaining set to games with a measurable space of players, and show that for continuous convex games the core may be strictly included in the bargaining set but it coincides with the set of all countably additive payoff measures in the bargaining set. We provide examples which show that the continuity assumption is essential to our results

Core equivalence theorems for infinite convex games.

We show that the core of a continuous convex game on a measurable space of players is a von Neumann-Morgenstern stable set. We also extend the definition of the Mas-Colell bargaining set to games with a measurable space of players, and show that for continuous convex games the core may be strictly included in the bargaining set but it coincides with the set of all countably additive payoff measures in the bargaining set. We provide examples which show that the continuity assumption is essential to our results.

Bundling Equilibrium in Combinatorial auctions

This paper analyzes individually-rational ex post equilibrium in the VC (Vickrey-Clarke) combinatorial auctions. If $\Sigma$ is a family of bundles of goods, the organizer may restrict the participants by requiring them to submit their bids only for bundles in $\Sigma$. The $\Sigma$-VC combinatorial auctions (multi-good auctions) obtained in this way are known to be individually-rational truth-telling mechanisms. In contrast, this paper deals with non-restricted VC auctions, in which the buyers restrict themselves to bids on bundles in $\Sigma$, because it is rational for them to do so. That is, it may be that when the buyers report their valuation of the bundles in $\Sigma$, they are in an equilibrium. We fully characterize those $\Sigma$ that induce individually rational equilibrium in every VC auction, and we refer to the associated equilibrium as a bundling equilibrium. The number of bundles in $\Sigma$ represents the communication complexity of the equilibrium. A special case of bundling equilibrium is partition-based equilibrium, in which $\Sigma$ is a field, that is, it is generated by a partition. We analyze the tradeoff between communication complexity and economic efficiency of bundling equilibrium, focusing in particular on partition-based equilibrium