Solving a game differently
Gisèle Umbhauer · 2016
This chapter focuses on trembles and their consequences, and the core concept developed is Selten&s;s trembling-hand equilibrium. Selten doesn&s;t shake the whole game: he only perturbs strategies. His idea is that the chapter push on a button to validate the strategy, and that with a small probability because of distraction or temporary insanity, or a trembling hand, it pushes on a wrong button. The chapter talks about Selten&s;s closest related concepts, Kreps and Wilson&s;s sequential equilibrium and Harsanyi&s;s perfect Bayesian equilibrium. It proposes four nice examples that show in a progressive way when very small changes have no impact and when, by contrast, they can destroy upper hemicontinuity and lower hemicontinuity of equilibrium sets. The chapter works with a carrier pigeon, and studies successively an ascending all pay auction with unknown budgets, negotiation games with an unknown number of negotiation rounds, and Rubinstein&s;s electronic mail game. It perturbs payoffs with Jackson et al. and the concept of quantal response.