Chapter 3 - Dominant strategies and the role of the law

Repetition - elements of the game

• player

• action (and strategies)

• payoffs

• information

Solve the game:

Identify the strategies that individuals will rationally and predictably choose

Find one strategy for each player that these individuals habe no incentive to abandon in favor of other strategies —> equilibrium strategies

Describe the expected payoffs that individuals expect at the end of the interaction

2 types of equilibrium:

• Dominant strategy equilibrium

• Nash equilibrium

Equilibrium of dominant strategies - Individuals best response

best response to the strategies of others. (I chose a strategy that gives me best payoff depending on what the other player choses)

Equilibrium of Dominant strategies - Strongly dominant strategy

I chose the same strategy - independently of what other players chose. This strategy is the best response to any strategies that others may select. - this is a strictly dominant strategy

The other strategies not chosen are dominated

The focus in this chapter is non-dymanic interactions, with complete but imperfect information. describe!

Static: decisions at the same time (the order does not matter)

Complete information: all players know the structure of the game, including

• payoffs for each players

• strategies available for each player

• The preference/goals of each player

Imperfect: no player knows what has happened in the game till this point

Iterative dominance equilibrium

a combination of strategies determined by successive eliminations of strictly dominated strategies.

After each elimination, the remaining strategies are compared again, to eliminate those that can be identified as dominated

The process ends when only one strategy remains for each player

problem with iterative dominance equilibrium

1. At each stage, common knowledge must be assumed: that other players are rational and will never chose dominated strategies

2. If strictly dominant strategies cannot be identified for one or more players:

   • Its difficult to know which strategies to eliminate

   • its hard to determine one equilibrium —> multiple equilibriums? - nash equilibrium(?)

The role of the law in determining balance of dominant strategies

Example with car drived and cyclist - drive carefully or not carefully?

If no law - both drivers will chose “without care”

If a law that puts the burden on the car driver if there is an accident - both will still chose without care

If a lawthat suggest that car driver is only liable is cyclist is careful, and car driver is not? - both will bow chose with care! (see notes for full presentation of best choice)