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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.
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.
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.
Example 6.1 Consider a two-player game in which each player selects a natural num-ber ∈ N = {0 1 2 }, and the payoff of each player is 1 2. It is easy to check that (0 0) is a Nash equilibrium, and there is no other Nash equilibrium. Nevertheless, all strategies, including 0, are weakly dominated.
