Abstract
Considered are perfect information games with a borel measurable payoff function that is parameterized by points of a polish space. The existence domain of such a parameterized game is the set of parameters for which the game admits a subgame perfect equilibrium. We show that the existence domain of a parameterized stopping game is a borel set. In general, however, the existence domain of a parameterized game need not be borel, or even an analytic or co-analytic set. We show that the family of existence domains coincides with the family of game projections of borel sets. Consequently, we obtain an upper bound on the set-theoretic complexity of the existence domains, and show that the bound is tight.
Original language | English |
---|---|
Pages (from-to) | 683-699 |
Number of pages | 17 |
Journal | Annals of Operations Research |
Volume | 287 |
Issue number | 2 |
Early online date | 28 Oct 2018 |
DOIs | |
Publication status | Published - Apr 2020 |
Keywords
- game projection
- parameterized games
- perfect information games
- subgame perfect equilibrium
- CLASSICAL HIERARCHIES
- Game projection
- Parameterized games
- EQUILIBRIUM
- Subgame perfect equilibrium
- MODERN STANDPOINT
- Perfect information games