Economics 112
Lecture Notes
Lecture 2. Equilibrium
This lecture sets out a number of
solution concepts
for games and illustrates their
application in a set of classic games. Key terms: Dominant strategy; best response;
cooperative solution; Nash equilibrium; focal point; zero sum game.
So far we have concentrated on turning a description of a strategic situation into a formal
representation, but have not said much about what happens in the game. Here we begin to
solve games, to make a prediction about what happens. The solutions we find are referred to
as equilibriums (or equilibria) of one kind or another. For the most part, we focus on
non
cooperative
solutions: that is, we assume that the players choose strategies looking to their
own interest, and are unable to commit to making choices that do not work in their own
interest.
We will also concentrate for the time being on rational players, choosing strategies
to achieve preferred outcomes. You will see that there are other interpretations of game
theory, notably evolutionary models.
Dividing the analysis of a game into a specification step followed by a solution step is useful.
Getting the specification correct is often the hardest part, and criticizing the results of an
application of game theory by trying to deny the logic of the solution method is usually less
fruitful that reexamining the specification. But this separation is not absolute: in some cases
there will be a number of potential solution concepts. In these cases, the choice of a solution
concept is itself part of the game specification.
1. Best responses
Rational players in noncooperative games survey the available strategies, and choose the one
that leads to the most preferred outcome.
A player’s
best response
is the strategy that
yields the highest payoff, given the strategies chosen by the other players. For example,
consider the two player game illustrated below.
First assume that player 2 is playing Left. Then player 1 can choose Up, for a payoff of 2, or
Down for a payoff of 3. Since Down yields the highest payoff, we say that Down is the best
response to Left. You should work out the other possible best responses. For example, you
should convince yourself that Right is player 2’s best response to Down.
Copyright David Scoones 2010
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View Full DocumentIf you did what I just told you to do, you will have noticed that best responses need not be
unique: two (or more) strategies may lead to the same payoff, given the strategies chosen by
other players. For this reason, the assumption that players choose best responses does not
always isolate a specific choice. Less obvious is that best responses may not exist. That is, it
may be that no strategy is truly best, given the choices made by other players. This won’t
happen in examples like the one above, but can in some not so well formed games.
Technical assumptions that guarantee a game will have well defined best responses are
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 Winter '08
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 Economics, Game Theory, best response, Copyright David Scoones

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