# Strategic interactions: Game theory; discussion and overview

## 5.17 Some video lectures covering much of the material in the next sections, but less formally

Note: These videos might only be available to Exeter students

1. Brief introduction to game theory

(Starting at 1:26:15)

1. Most of the material (notes/board based)
1. Backwards induction, games with infitite action spaces, discussion of laboratory experiments

See outline

## 5.19 Introduction

We considered decisions under ‘natural’ uncertainty (known probability distributions), considering preferences and choices, and concepts such as ‘expected utility’ and ‘risk aversion’.

Much of microeconomics also considers the prices and outcomes in markets with many individual consumers and firms. We consider concepts such as (Walrasian) equilibrium.

Now we also want to consider $\rightarrow$ Strategic uncertainty: one “agent’s” best choice may depend on what others choose, but each agent may be unsure about what others will choose.

Furthermore, we may have interactions among only a small number of agents, so (unlike in large markets) each agent’s choice may affect the payoffs of other agents (and, in sequential games, may influence their choices).

$\rightarrow$ Game Theory is one of the the main approaches that Economists (and others) use to consider such situations, and what choices might be made.

Is game theory useful???

Some people seem to think so:

### 5.19.1 Basic concepts (strategic interaction, elements of a game))

In ‘large markets with many small players’: Each individual (consumer, firm, etc) takes all others’ choices as given

• market price, demand curve, etc.

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Now: Consider ‘strategic interaction’

• My best choice may depend on your choice
• And vice versa
• Sequential games: My earlier choices may change your later choices

### 5.19.2 Some examples

Is it better to get lunch at Comida or Pret?

2020-21 Exeter students: if this were a normal year this question qould make more sense.

• What if your friends are going to Comida?

• What if everyone and her cousin are going to Comida, so the queue is miles long?

What should Tim Cook charge for his new Iphone?

• Does it depend on whether Samsung and LG…

… Sell their phones for £200, or £1000, or go out of business?

Find a situation in business, government, fiction, history or your own life where one party’s optimal choice depends on what another party does.

Write it down, give a 1-sentence explanation of why it involves ‘strategic dependence’

Some possible examples:

Life:

Politics:

• Country makes war or peace? Soldiers fight or run away?

• Run for office or not? Party contests a seat? If so, how much to spend on campaign?

Standard Economics:

• Amount to bid at a first-price auction?

• Whether Firezza pizza opens a new branch in Exeter, and where?

• How hard to work towards a promotion at your job?

Very interesting problems, do Economics and Game Theory have the solutions?

### What game theory can do (wet blanket)

Game theory gives us a language and framework for analyzing strategic situations

The ‘solution concepts’ can be said to make ‘predictions’ under given assumptions. The idea of ‘equilibrium’ is defined as a baseline.

Dr. Reinstein says: Sometimes overrated as a tool for predicting how people/firms will actually behave.

• It often makes multiple predictions, or predicts ‘mixed strategies’ (randomisation).

• Real-world and experimental choices are often/arguably predicted poorly by classical game theory.

• For example, standard game theory says chess has a pre-determined outcome and is a bit boring (ok, you may agree about the latter).

Adv: But there are complicating issues making it difficult to asses the ‘predictions’ of game theory.

Particularly because monetary payoff may not be the same as utility payoffs … this can make real-world predictions unclear.

Particularly if there are social preferences or fairness preferences.

We also see failures to coordinate, failure to take higher-order cognitive steps, and preferences over the manner decisions are made. These make Game Theoretic predictions difficult.