We analyze three games using our new solution concept, subgame perfect equilibrium (SPE). theory. Consider the strategies: 1:play nc in every stage For finite games of perfect information, any backward induction solution is a SPNE and vice-versa. 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 first game involves players’ trusting that others will not make mistakes. The whole game. This remains an SPNE outcome of the infinitely repeated game. Game Theory Chris Georges Some Notation and Definitions 1. This game has 3 subgames: The game 2 plays if 1 plays A. Lecture 19 - Subgame Perfect Equilibrium: Matchmaking and Strategic Investments Overview. 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 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. Not all NE are SPNE. The game 1 plays if 1 plays B. 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 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. Notice that every SPNE must also be a NE, because the full game is also a subgame. ECON 159: Game Theory. A is a best response if and only if the player assigns at most prob 1=2 The Normal Form Representation ... a NE for each subgame of the game. The ad-vantage of SPNE is that it can be applied to games of imperfect information too. To find the Subgame Perfect Nash equilibrium, we need to solve for the nash equilibria of each subgame. In the subgame identified in 1, player 2 plays C, because $4>2$. 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. 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. 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) In the subgame identified in 2, $(E,X)$ is the unique nash equilibrium. sub-game it finds itself in. 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.

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