Abstract
The concept of subgame perfect -equilibrium (-SPE), where is an error-term, has in recent years emerged as a prominent solution concept for perfect information games of infinite duration. We propose two refinements of this concept: continuity -SPE and -tolerance equilibrium. A continuity -SPE is an -SPE in which, in any subgame, the induced play is a continuity point of the payoff functions. We prove that continuity -SPE exists for each if the payoff functions are bounded and lower semicontinuous. A loss tolerance function is a function that assigns to each history a positive real number . A strategy profile is said to be a -tolerance equilibrium if for each history it is a -equilibrium in the subgame starting at . We prove that, for each loss tolerance function , there exists a -tolerance equilibrium provided that the payoff functions are bounded and continuous. We give counterexamples to show the sharpness of the existence results.
Original language | English |
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Pages (from-to) | 523-542 |
Number of pages | 20 |
Journal | International Journal of Game Theory |
Volume | 45 |
Issue number | 3 |
DOIs | |
Publication status | Published - Aug 2016 |
Keywords
- Perfect information games
- Subgame perfect equilibria
- Discontinuous games
- EXISTENCE
- INFORMATION GAMES
- STOCHASTIC GAMES
- INFINITE-HORIZON
- SEMICONTINUOUS PAYOFFS
- QUITTING GAMES