Mathematics

### Material on Test 2

Test 2 is Friday Nov. 9. It will cover chapters 4 to 8 in the online notes. (Omit 4.2, 5.9 - 5.10, 6.1 - 6.4, 6.7, 8.1 - 8.2.)

Things you should be able to do:
• For games in which Nature moves, (1) draw the game tree, (2) construct the normal form of the game, in which the payoffs are expected payoffs, (3) analyze the normal form of the game as usual (look for dominated strategies, Nash equilibria). (Problem 4.7.2.)

• Find mixed-strategy Nash equilibria. (Problems 5.11.1 to 5.11.6.)

• For certain infinitely repeated games, show that, if the discount factor delta is large enough, it is a Nash equilibrium for every player to use a trigger strategy. (Problems 6.8.2 and 6.8.3.)

• For a symmetric n-person normal-form game, find Nash equilibria. (Problems 7.3.1 to 7.3.3.)

• For a symmetric two-person normal-form game, check whether symmetric Nash equilibria correspond to evolutionarily stable states. (Problems 8.6.1 and 8.6.3. I will write Theorem 8.5 on the board if it's needed.)

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