Game Theory Chris Georges Some Notation and Definitions 1. The first game involves players’ trusting that others will not make mistakes. For example the following is an SPE for this game: S1(†) = R;S2(h) = (L0 h = R R0 h = L This SPE strategy has P2 behave according to which subgame (Left or Right) it finds itself in, and provides the best response in that subgame. theory. To find the Subgame Perfect Nash equilibrium, we need to solve for the nash equilibria of each subgame. sub-game it finds itself in. The ad-vantage of SPNE is that it can be applied to games of imperfect information too. In the subgame identified in 2, $(E,X)$ is the unique nash equilibrium. stated in the beginning of the class implies that there is a unique SPNE in the finite repetition of this game, namely in each and every stage. Beliefs and optimal strategies a ecting each other The following game has no proper subgames: Beliefs a ect optimal strategies:consider pl 2 in info set fM;Rg. In game theory, the centipede game, first introduced by Robert Rosenthal in 1981, is an extensive form game in which two players take turns choosing either to take a slightly larger share of an increasing pot, or to pass the pot to the other player. In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games.A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. This remains an SPNE outcome of the infinitely repeated game. The Normal Form Representation ... a NE for each subgame of the game. We analyze three games using our new solution concept, subgame perfect equilibrium (SPE). At a NE that is not a SPNE, some player is playing a strategy that is a BR in ... game (of complete information) must have at least one SPNE. In the subgame identified in 1, player 2 plays C, because $4>2$. Mark Voorneveld Game theory SF2972, Extensive form games 18/25. • Since the whole game is always a subgame, every SPNE is a Nash equilibrium, we thus say that SPNE is a refinement of Nash equilibrium • Simultaneous move games have no proper subgames and thus every Nash equilibrium is subgame perfect • SPNE can be found using a simple algorithm known as backward induction (cf Zermelo 1913) This game has 3 subgames: The game 2 plays if 1 plays A. Dynamic Game Theory Equilibrium concept Some NEs are odd in the dynamic context • so there’s a need to refine equilibrium concept Introduce Subgame -Perfect Nash Equilibrium (SPNE) A profile of strategies is a SPNE for a game if it • is a NE • induces actions consistent with NE in every subgame April 2018 24 The whole game. Not all NE are SPNE. For finite games of perfect information, any backward induction solution is a SPNE and vice-versa. Lecture 19 - Subgame Perfect Equilibrium: Matchmaking and Strategic Investments Overview. 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