Game Theory Optimal Strategy
In game theory, a trigger strategy is any of a class of strategies employed in a repeated non-cooperative game. A player using a trigger strategy initially cooperates but punishes the opponent if a certain level of defection (i.e., the trigger) is observed.
Thus C’s optimal strategy is given by 2=7 5=7 Since the expected pay-o is given by 29=7 + 7(p 3=7)(q 2=7), the value of the game is given by = 29=7 (when both players play their optimal strategy). Optimal Mixed Strategies and the Value of a Zero-Sum Game with no saddle point. Strategy profile sis Pareto optimal, or strictly Pareto efficient, if there’s no strategy s' that Pareto dominates s Every game has at least one Pareto optimal profile Always at least one Pareto optimal profile in which the strategies are pure Nau: Game Theory 9. Bidding at Auction. An auction is considered as a sale activity in which different bidders bid for.
The strategy corresponding to the Nash equilibrium is an optimal mixed strategy in ∆. Since game ∆ is fair (i.e. Its value is 0 and the sets of optimal strategies for the first and second player are the same), an optimal mixed strategy can be found by the solution of some linear feasibility problem. Pure and Mixed Strategies: In a pure strategy, players adopt a strategy that provides the best.
The level of punishment and the sensitivity of the trigger vary with different trigger strategies.
Trigger strategies[edit]
Game Theory Explained
- Grim trigger (the punishment continues indefinitely after the other player defects just once)
- Tit for tat (the punishment continues as long as the other player defects)
- Tit for two tats (a more forgiving variant of tit for tat)
References[edit]
- Textbooks and general reference texts
- Vives, X. (1999) Oligopoly pricing, MIT Press, Cambridge MA (readable; suitable for advanced undergraduates.)
- Tirole, J. (1988) The Theory of Industrial Organization, MIT Press, Cambridge MA (An organized introduction to industrial organization)
- Classical paper on this subject
- Friedman, J. (1971). A non-cooperative equilibrium for supergames, Review of Economic Studies 38, 1–12. (The first formal proof of the Folk theorem (game theory)).
