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Mixed Strategy Nash Equilibrium. Definitions. Example 1: Public Goods Provision. Example 2: Defense against Terrorism. Choice Under Uncertainty. So far we have been talking about preferences over certain alternatives. Let’s think about preferences over what might be called “risky” alternatives.
Mixed strategies. Mixed strategy Nash equilibrium. Existence of Nash equilibrium. Examples. Discussion of Nash equilibrium Notation: Given a set X, we let Δ(X) denote the set of all probability distributions on X. Given a strategy space S for player i, mixed strategies for player i are Δ(S the. i) Idea: a player can randomize over pure strategies.
Example 3.4.1 : Matching Pennies Game. Consider the game in which each player can choose HEADS (H) or TAILS (T); if the two players match, Player 1 wins; if the two players differ, Player 2 wins. What strategy should each player play?
Example taken from Game Theory and Strategy (Straffin 1993) p.16. Three Methods for Solving Mixed Strategy Solutions. Method of Equalizing Expectation: A mixed strategy for the column player must result in equivalent payoff in active row strategies. Results in solving simultaneous linear equations.
Solutions. Departament of Economics. Problem 1: For each one of the following normal form games find. The pure-strategy Nash equilibria and their payofs; The mixed-strategy Nash equilibria and their payofs; Are there any equilibria in dominant strategies? If yes, which ones? A. B. Solution: The best responses of the players are.
In this section we will learn a method for finding the maximin solution for a repeated game using a graph. Let's continue to consider the game given in Example 3.1.1 3.1.1 by. [ 1 −1 0 2] [ 1 0 − 1 2] In order to make our analysis easier, let's name the row and column strategies as in Table 3.2.1 3.2.1.
Finding Mixed-Strategy Nash Equilibria. Let’s look at some examples and use our lesson to nd the mixed-strategy NE. Example 1 Battle of the Sexes a b A 2;1 0;0 B 0;0 1;2 In this game, we know that there are two pure-strategy NE at (A;a) and (B;b). Let’s see if there are any other mixed-strategy NE.
