Applications and Limits of Game Theory

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Applications and Limits of Game Theory

game theory explains why things happen

illustration : side-botched lizzards

		Player X
		rock	paper	scissors
Player Y	rock	0 0	-1 1	1 -1
	paper	1 -1	0 0	-1 1
	scissors	-1 1	1 -1	0 0

‘Each of two people chooses either Head or Tail. If the choices differ, person 1 pays person 2 a dollar; if they are the same, person 2 pays person 1 a dollar. Each person cares only about the amount of money that he receives. A game that models this situation is shown in Figure 17.3. Such a game, in which the interests of the players are diametrically opposed, is called “strictly competitive”. The game Matching Pennies has no Nash equilibrium’ (Osborne & Rubinstein, 1994).

Can you identify the nash equilibira?

There are none!

Sinervo & Lively (1996)

I couldn’t resist this one ... game theory (rock-paper-scissors specifically) has been used to explain ‘evolutionary stable strategy model to a three-morph mating system in the side-blotched lizard’ (Sinervo & Lively, 1996). (The ones on the right resemble sexually receptive females morphologically; they are ‘sneakers’.)

aside: Where do the preferences come from?

limited range of actions

∴ not decision theory

In this case we are not relying on decision theory (limited range of actions)

task : find cases where game theory explains things

in law: inequality, culture and power (McAdams, 2008)
network security (Roy et al., 2010)
evolution of social contract (Skyrms, 2000)

‘evolutionary models supply a rationale for Nash equilibrium that rational choice theory is hard-pressed to deliver. Furthermore, in cases with multiple symmetrical Nash equilibria, the dynamic models offer a plausi- ble, historically path-dependent model of equilibrium selection’ (Skyrms, 2000)

distribution of water resources (Madani, 2010)
the tragedy of the commons Tadelis (2013, p. §5.2.2)
foraging behaviours (Hansen, 1986)
...

Interesting question about each of these cases: What is it that has preferences? On what basis are the preferences assigned?

game theory

Aim: describe rational behaviour in social interactions.

Or does it?

weak dominance strict dominance dominance

cutthroat competition in business is the result of the rivals being trapped in a prisoners’ dilemma’

(Dixit, Skeath, & Reiley, 2014, p. 36).

(Dixit et al., 2014, p. 36)

pd is a good target because common.

Games with the Prisoner’s Dilemma structure arise in:

bower birds (maraud/guard nests)

business organisations (product pricing)

countries (international environmental policy)

individual adult humans (suspects under arrest)

(Dixit et al., 2014, p. chapter 10)

Start by explaining dominance (simpler than a nash equilibrimm)

		Prisoner X
		resist	confess
Prisoner 59640	resist	3 3	0 4
	confess	4 0	1 1

observation: people in this kind of situation will rationally end up performing actions which are mutually harmful in the sense that there is a better course of actions available to them.

game theory -> always get a worst outcome in pd

game theory

Aim: describe rational behaviour in social interactions.

Just here we are moving from applications to limits (with hardly a break ...)

short essay question:

What is team reasoning?

Which, if any, social interactions are better modeled by team reasoning than game theory?

plan

1. What is game theory? ✓

1a. What are its applications? ✓

2. What are its limits? ✓

3. What is team reasoning and how might it overcome the limits? ✓

game theory

Aim: describe rational behaviour in social interactions.

		Player X
		high	low
Player Y	high	2 2	0 0
	low	0 0	1 1

This game has two nash equilibria ...

A nash equilibrium for a game is a set of actions from which no agent can unilaterally profitably deviate

(Osborne & Rubinstein, 1994, p. 14).

An action is rational
in a noncooperative game
if it is a member of a nash equilibrium?

Maybe this idea isn’t very plausible. It seems to get PD wrong (it says that an apparently rational course of action (resist) is nonrational) and it seems to get hi-low wrong (it says that an apparently nonrational action (low) is no less rational than an apparently rational action (high).)

game theory

Aim: describe rational behaviour in social interactions.

‘understanding why game theory does not, in the end, constitute the science of society (even though it comes close) is terribly important in understanding the nature and complexity of social processes’

(Hargreaves-Heap & Varoufakis, 2004, p. 3)

some applications of game theory succeed, others might fail

Just here we are moving from applications to limits (with hardly a break ...)

short essay question:

What is team reasoning?

Which, if any, social interactions are better modeled by team reasoning than game theory?

plan

1. What is game theory? ✓

1a. What are its applications? ✓

2. What are its limits? ✓

3. What is team reasoning and how might it overcome the limits? ✓

PS

Maybe there are other kinds of eqilibrium?

(Hargreaves-Heap & Varoufakis, 2004, p. 3)

also: evolutionary game theory Skyrms (2000)

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Applications and Limits of Game Theory

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