Game Development Reference

In-Depth Information

in every situation and all the players in the game. This is not always

reasonable in, for example, the large auctions played over the internet.

•

Nash equilibrium presumes that players know what other players are

doing (and are making a best response to it). But how do they gain this

knowledge in a one-shot game, particularly if there are multiple equilibria?

In the following sections, I discuss each of these issues in more detail, and

sketch solution concepts that can deal with them, with pointers to the relevant

literature.

8.2 Robust and resilient equilibrium

Nash equilibrium tolerates deviations by one player. It is perfectly consistent

with Nash equilibrium that two players could do much better by deviating in

a coordinated way. For example, consider a game with
n>
1 players where

players must play either 0 or 1. If everyone plays 0, everyone gets a payoff of

1; if exactly two players play 1 and the rest play 0, then the two who play

1 get a payoff of 2, and the rest get 0; otherwise, everyone gets 0. Clearly

everyone playing 0 is a Nash equilibrium, but any pair of players can do

better by deviating and playing 1.

Say that a Nash equilibrium is
k
-resilient
if it tolerates deviations by

coalitions of up to
k
players. The notion of resilience is an old one in the

game theory literature, going back to Aumann [1959]. Various extensions of

Nash equilibrium have been proposed in the game theory literature to deal

with coalitions [Bernheim et al., 1989, Moreno and Wooders, 1996]. However,

these notions do not deal with players who act in unexpected ways.

There can be many reasons that players act in unexpected ways. One, of

course, is that they are indeed irrational. However, often seemingly irrational

behaviour can be explained by players having unexpected utilities. For

example, in a peer-to-peer network like Kazaa or Gnutella, it would seem

that no rational agent should share files. Whether or not you can get a

file depends only on whether other people share files. Moreover, there are

disincentives for sharing (the possibility of lawsuits, use of bandwidth, etc.).

Nevertheless, people do share files. However, studies of the Gnutella network

have shown that almost 70 percent of users share no files and nearly 50

percent of responses are from the top 1 percent of sharing hosts [Adar and

Huberman, 2000]. Is the behaviour of the sharing hosts irrational? It is if

we assume appropriate utilities. But perhaps sharing hosts get a big kick

out of being the ones that provide everyone else with the music they play.

Is that so irrational? In other cases, seemingly irrational behaviour can be

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