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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.
Exercise 3.4.17 : Solve a \ (2\times 2\) Repeated Game Using Expected Values. Apply this method of using expected value to Example \ (3.1.1\) (which we solved using the graphical method in the previous section) to find the equilibrium mixed strategies for each player and the value of the game for each player:
Mixed Strategies: Graphical Solution; Using Sage to Graph Lines and Solve Equations; Mixed Strategies: Expected Value Solution; Liar's Poker; Augmented Matrices; Undercut; 4 Non-Zero-Sum Games. Introduction to Two-Player Non-Zero-Sum Games; Prisoner's Dilemma and Chicken; A Class-Wide Experiment; What Makes a Prisoner's Dilemma? Another ...
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 by. [ 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.
Figure 16.16 Full computation of the mixed strategy. For example, if the Man (row player) goes to the Baseball game, he gets 3 when the Woman goes to the Baseball game (probability p ), and otherwise gets 1, for an expected payoff of 3 p + 1 (1 – p) = 1 + 2 p.
a mixed strategy is one where a player plays (some of) the available pure strategies with certain probabilities. concept best understood in repeated games, where each player’s aim is to keep the other guessing. Examples: Rock–Scissors–Paper game, penalty kicks, tennis point, bait cars, tax audits, drug testing. etc.
