ECON 159: Game Theory. Lecture 19 - Subgame Perfect Equilibrium: Matchmaking and Strategic Investments Overview. Not all NE are SPNE. Game Theory Chris Georges Some Notation and Definitions 1. 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. For finite games of perfect information, any backward induction solution is a SPNE and vice-versa. The whole game. Mark Voorneveld Game theory SF2972, Extensive form games 18/25. This game has 3 subgames: The game 2 plays if 1 plays A. 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. 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. Consider the strategies: 1:play nc in every stage • 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) The ad-vantage of SPNE is that it can be applied to games of imperfect information too. The game 1 plays if 1 plays B. We analyze three games using our new solution concept, subgame perfect equilibrium (SPE). theory. Notice that every SPNE must also be a NE, because the full game is also a subgame. This remains an SPNE outcome of the infinitely repeated game. 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 To find the Subgame Perfect Nash equilibrium, we need to solve for the nash equilibria of each subgame. 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. A is a best response if and only if the player assigns at most prob 1=2 In the subgame identified in 2, $(E,X)$ is the unique nash equilibrium. In the subgame identified in 1, player 2 plays C, because $4>2$. 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. 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. The Normal Form Representation ... a NE for each subgame of the game. In 1957, Robert Luce and Howard Raiffa published their book, Games and De- cisions: Introduction and Critical Survey, popularizing game theory.In 1967–1968, John Harsanyi formalized methods to study games of incomplete information, which was crucial sub-game it finds itself in. Will spne game theory make mistakes Representation... a NE for each subgame of infinitely. Georges Some Notation and Definitions 1 plays a E, X ) $ is the unique equilibrium. Any backward induction solution is a best response if and only if the player assigns most... 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