Topic 3 Key concepts

Question 1

Nash equilibrium of a game (the two definitions)

Answer 1

A Nash equilibrium (NE) of a game is a combination of strategies, one for each player, such that the strategy of any player is a best response to her opponents’ strategies.
In a Nash equilibrium (NE) no player has a profitable unilateral deviation, that is, no player can get a better payoff by unilaterally switching to some other available strategy while all the other players adhere to the strategies specified for them in the list.
(In a NE, no player regrets his/her strategy, given everybody else’s strategies (even if you are not necessarily happy with the other players’ strategies))

Question 2

Coordination games and risk-dominant equilibrium

Answer 2

PURE COORDINATION GAMES: Common interests, but independent choices. (With previous communication, there is no strategic problem. But, without communication, you need a focal point.)
Coordination games where there is a conflict between efficiency and risk, there is always a safe strategy and a risky strategy for each player (but the risky strategy yields the efficient outcome if everybody plays it).

The risk-dominant NE is the equilibrium in which the players choose the action that is their best response if they expect that his opponent will play both actions with equal probability

Question 3

A game with a Chicken game structure

Answer 3

Four essential features:
1. Each player has one strategy that is the “tough” strategy and one that is the “weak” strategy.
2. There are two NE. These are the outcomes in which exactly one of the players is weak.
3. Each player strictly prefers that equilibrium in which the other player chooses weak.
4. The payoffs when both players are tough are very bad for both players.
- There is a “first-mover advantage”: if you can make an observable and irrevocable first move, then you get your preferred equilibrium.

Question 4

Social Preferences

Answer 4

A player has social (non-selfish) preferences if he cares not only about his absolute material payoff, but also about other factors, for example: Relative payoffs (the distribution of payoffs between players), social welfare (efficiency), fairness…
- Examples: Inequity aversion, altruism…

Question 5

Inequity aversion

Answer 5

A very common social preference in society is inequity aversion: we do not only care about our payoffs but also about our payoffs in comparison to others’. Receiving a different payoff than others causes us disutility, (and this disutility is greater if our payoff is lower than others’ (disadvantageous inequity aversion) than if it is higher (advantageous inequity aversion)).