## How do you find subgame perfect equilibrium backward induction?

To solve this game, first find the Nash Equilibria by mutual best response of Subgame 1. Then use backwards induction and plug in (A,X) → (3,4) so that (3,4) become the payoffs for Subgame 2. The dashed line indicates that player 2 does not know whether player 1 will play A or B in a simultaneous game.

What is backward induction equilibrium?

What Is Backward Induction? Backward induction in game theory is an iterative process of reasoning backward in time, from the end of a problem or situation, to solve finite extensive form and sequential games, and infer a sequence of optimal actions.

What is the difference between subgame perfect Nash equilibrium and Nash equilibrium of an extensive form game?

The key difference between subgame perfect equilibrium and Nash equilibrium is that subgame perfect equilibrium require that all threats are credible. Consequently, the study of subgame perfect equilibrium is the study of credible threats. Subgame perfect equilibria are a subset of Nash equilibria.

### How do you find Subgames?

A well-defined subgame starts at x if and only if each information set h of the original game is a subset of Vx or is a subset of its complement. Since extensive form games with imperfect information need not have proper subgames, the notion of subgame perfection typically has little ‘bite’.

What is backward induction in dynamic programming?

Backward induction is the process of reasoning backwards in time, from the end of a problem or situation, to determine a sequence of optimal actions. It proceeds by examining the last point at which a decision is to be made and then identifying what action would be most optimal at that moment.

What is backward induction quizlet?

Backward induction. an iterative process for solving finite extensive form or sequential games. First, one determines the optimal strategy of the player who makes the last move of the game. Then, the optimal action of the next-to-last moving player is determined taking the last player’s action as given.

#### Can you do proof by induction backwards?

Here are some possibilities: Backwards induction: start with base case n = N and go backwards, instead of starting at base case n = 1 and going forwards. Two-step induction, where the proof for n = x + 1 relies not only on the formula being true for n = x, but also on it being true for n = x − 1.

What is the subgame perfect Nash equilibrium quizlet?

A Nash equilibrium of an extensive form game is a subgame perfect equilibrium if it induces Nash equilibrium play in every subgame. Nash equilibria that do not involve any incredible threats or promises in any part of any player’s strategy are called subgame perfect.

How many subgame perfect equilibria are there?

Most games have only one subgame perfect equilibrium, but not all. When players receive the same payoff for two different strategies, they are indifferent and therefore may select either. This causes multiple SPE.

## What is a subgame game theory?

In game theory, a subgame is a subset of any game that includes an initial node (which has to be independent from any information set) and all its successor nodes. It’s quite easy to understand how subgames work using the extensive form when describing the game.

What is the subgame perfect equilibrium through backwards induction?

Thus, the subgame perfect equilibrium through backwards induction is (UA, X) with the payoff (3, 4). For finitely repeated games, if a stage game has only one unique Nash equilibrium, the subgame perfect equilibrium is to play without considering past actions, treating the current subgame as a one-shot game.

What is a subgame perfect Nash equilibrium?

A subgame perfect Nash equilibrium is an equilibrium such that players’ strategies constitute a Nash equilibrium in every subgame of the original game. It may be found by backward induction, an iterative process for solving finite extensive form or sequential games.

### What is the subgame perfect equilibrium in chess?

Every finite extensive game with perfect recall has a subgame perfect equilibrium. Perfect recall is a term introduced by Harold W. Kuhn in 1953 and “equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves”.

Which games have the best backward induction strategies?

One game in which the backward induction solution is well known is tic-tac-toe, but in theory even Go has such an optimum strategy for all players.