Abstract
For the assignment game, we propose the following selling mechanism: sellers, simultaneously, fix their prices first; then buyers, sequentially, decide which object to buy, if any. The first phase of the game determines the potential prices, while the second phase determines the actual matching. We prove that the set of subgame perfect equilibria in pure strategies in the strong sense of the mechanism coincides with the set of sellers' optimal stable outcomes when buyers use maximal strategies.
Highlights
In their seminal contribution, Gale and Shapley (1962) introduce the study of markets where agents from two distinct groups meet
We investigate the result of non-cooperative behavior by sellers and buyers in the assignment game
We look for the subgame perfect equilibria in pure strategies (SPE) of the previous mechanism
Summary
The equilibria of the selling mechanism; 5. We propose the following selling mechanism: sellers, simultaneously, fix their prices first; buyers, sequentially, decide which object to buy, if any. We prove that the set of subgame perfect equilibria in pure strategies in the strong sense of the mechanism coincides with the set of sellers’ optimal stable outcomes when buyers use maximal strategies. Propomos o seguinte mecanismo para o assignment game: os vendedores, simultaneamente, fixam seus precos. A primeira fase do jogo determina os precos dos objetos que forem vendidos, enquanto a segunda fase determina o matching real. Provamos que o conjunto dos equilıbrios perfeitos de subjogo em estrategias puras no sentido forte, do jogo induzido pelo mecanismo, coincide com o conjunto dos resultados estaveisotimos para os vendedores quando os compradores usam estrategias maximais
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