Games and Strategies Lecture 3

What is Nash Equilibrium?

1) Nash Equilibrium occurs where the players chose a strategy that best responds to their opponent's strategy. 2) It occurs where player 1 cannot make themselves better off by choosing a different strategy, given the strategy choice of player 2- same for player 2. 3) Hence, the players coordinate on a single strategy profile- ∴ there is no incentive to deviate and choose another strategy.

What are the conditions for a Nash Equilibrium?

A Nash equilibrium cannot be a strictly dominated strategy but can be a weakly dominated strategy.

What is meant by a Pareto dominant outcome?

A outcome will Pareto dominate another outcome if that outcome is weakly preferred by ALL players and strictly preferred by AT LEAST one player.

What is meant by the best response strategy for a player?

A strategy, s* is a best response strategy for a player to their opponent, if this strategy yields a weakly greater payoff that any other strategy.

What are the four types of coordination Nash Equilibrium games?

Convention game, Common interest game, Bargaining game, Constant-sum game.

Describe the Cournot Duopoly Model

There are two firms in the market, with inverse demand functions and assigned MCs. 1) Find the profit function for firm 1. 2) Differentiate the profit function wrt to q1- set it equal to 0. 3) Rearrange to make q1 the subject- THIS IS FIRM 1'S BEST RESPONSE FUNCTION/STRATEGY. 4) Work out the optimal quantity, price and profit. Do the same for firm 2.

What is meant by a Pareto Optimal or Pareto Efficient outcome?

When an outcome is not Pareto dominatED by any other outcome- i.e. it is not weakly preferred by ALL players.

What is a convention game?

When there are multiple Nash equilibria that have equal payoffs.

What is a Bargaining game?

When there are multiple Nash equilibria, whereby the payoffs are NOT equal NOR Pareto ranked.

What is a common interest game?

When there are multiple Nash equilibria, whereby the payoffs are Pareto ranked.

What is meant by Pareto ranked outcomes?

Whereby an outcome is better than any other outcome for AT LEAST one player but is not worse for any of the players.

What is a constant-sum game?

Whereby the sum of all the players' payoffs is the same for any outcome- there is a mixed strategy Nash Equilibrium.