What Is Game Theory?

➢ Game theory is a method of analyzing strategic interaction.

➢ It is concerned with “how individuals make decisions when they are aware
that their actions affect each other and when each individual takes this into
account”

➢ Game theory is the study of how people behave in strategic situations.

➢ It's assumed players within the game are rational and will strive to maximize
their payoffs in the game.

➢ Game theory has a wide range of applications, including psychology,

evolutionary biology, war, politics, economics, and businesses.

➢ Businesses may use it, for example, to set prices, decide whether to acquire
another firm, and determine whether to go for new inventions or not.
 Who Came Up with Game Theory?

Game theory is largely attributed to the work of

mathematician John von Neumann and economist Oskar
Morgenstern in the 1940s.

Mathematician John Nash provided the first significant

extension of the von Neumann and Morgenstern work.
 Useful Terms in Game Theory

✓ Game: Any set of circumstances that has a result dependent on the actions of
two or more decision-makers (players).

✓ Players: A strategic decision-maker within the context of the game.

✓ Strategy: A complete plan of action a player will take given the set of
circumstances that might arise within the game.

✓ Payoff: The payout a player receives from arriving at a particular outcome.

The payout can be in any quantifiable form, from dollars to utility.

✓ Equilibrium: The point in a game where both players have made their
decisions and an outcome is reached.

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 Why game theory is important?

Interdependence Uncertainty

If I believe that my competitors are rational and act to

maximize their own payoffs, how should I take their
behavior into account when making my decisions?

Determining optimal strategies can be difficult, even

under conditions of complete symmetry and perfect
information.

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Why game theory is important?
 Noncooperative versus Cooperative Games

●Cooperative game Game in which participants can negotiate

binding contracts that allow them to plan joint strategies.

●Noncooperative game Game in which negotiation and enforcement of

binding contracts are not possible.

It is essential to understand your opponent’s point of view and to deduce his

or her likely responses to your actions.

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 1. Dominant Strategies
●Dominant strategy Strategy that is optimal no matter what an
opponent does.

Advertising is a dominant strategy for Firm A. The same is true for

Firm B: No matter what firm A does, Firm B does best by advertising. The
outcome for this game is that both firms will advertise.

●equilibrium in dominant strategies Outcome of a game in which each firm

is doing the best it can regardless of what its competitors are doing.

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 Unfortunately, not every game has a dominant strategy for each player.

Now Firm A has no dominant strategy. Its optimal decision depends on what
Firm B does. If Firm B advertises, Firm A does best by advertising; but if Firm B
does not advertise, Firm A also does best by not advertising.

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 2. The Nash Equilibrium Revisited
Dominant Strategies: I’m doing the best I can no matter what you do.
You’re doing the best you can no matter what I do.
Nash Equilibrium: I’m doing the best I can given what you are doing.
You’re doing the best you can given what I am doing.

1. Identify dominant strategy for Firm 1 & Firm 2?

2. Is there a existence of Nash equilibrium?

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 2. The Nash Equilibrium Revisited

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3. Maximin strategy (Maximum out of Minimum)

➢ This strategy is the decision to take the course of action which maximizes the minimum
possible pay-off.

➢ Since this decision criterion locates the alternative strategy that has the least possible
loss, it is also known as a pessimistic decision criterion.

The working method is:

(i) Determine the lowest outcome for each alternative.

(ii) Choose the alternative associated with the maximum of these.

Maximin strategy (Maximum out of Minimum)

Determine best action using maximin principle??

Maximin strategy (Maximum out of Minimum)
Maximin strategy (Maximum out of Minimum)

A business man has three alternatives open to him each of which can be followed by
any of the four possible events. The conditional pay offs for each action - event
combination are given below:

Determine which alternative should the businessman choose, if he adopts the maximin
principle?
Maximin strategy (Maximum out of Minimum)
4. Minimax strategy (Minimum out of Maximum)

This strategy is the decision to take the course of action which minimizes the maximum
possible pay-off. Since this decision criterion locates the alternative strategy that has
the greatest possible gain.

The working method is:

(i) Determine the highest outcome for each alternative.

(ii) Choose the alternative associated with the minimum of these.

Minimax strategy (Minimum out of Maximum)

Consider the following pay-off matrix

Using minimax principle, determine the best alternative.

Minimax strategy (Minimum out of Maximum)

Maximum
Payoff
 5. The prisoner’s dilemma

➢ Originally formulated by the American mathematician Albert W. Tucker.

➢ Two prisoners, A and B, suspected of committing a robbery together, are
isolated and urged to confess.
➢ Each is concerned only with getting the shortest possible prison sentence for
himself; each must decide whether to confess without knowing his partner’s
decision.
➢ Both prisoners, however, know the consequences of their decisions:
➢ (1) if both confess, both go to jail for five years;
➢ (2) if neither confesses, both go to jail for one year (for carrying concealed
weapons)
➢ (3) if one confesses while the other does not, the confessor goes free (for
turning state’s evidence) and the silent one goes to jail for 20 years.
 5. The prisoner’s dilemma

▪ Although A cannot be sure what B will do, he knows that he does best to confess
when B confesses (he gets five years rather than 20) and also when B remains
silent (he serves no time rather than a year); analogously, B will reach the same
conclusion.

▪ So the solution would seem to be that each prisoner does best to confess and go
to jail for five years.

▪ Paradoxically, however, the two robbers would do better if they both adopted
the apparently irrational strategy of remaining silent; each would then serve
only one year in jail.

▪ The irony of PD is that when each of two (or more) parties acts selfishly and
does not cooperate with the other (that is, when he confesses), they do worse
than when they act unselfishly and cooperate together (that is, when they
remain silent).
 OLIGOPOLISTIC COOPERATION IN THE WATER
METER INDUSTRY
For some four decades, almost all the water meters
sold in the United States have been produced by
four American companies: Rockwell International,
Badger Meter, Neptune Water Meter Company, and
Hersey Products.
Most buyers of water meters are municipal water
utilities, who install the meters in order to measure
water consumption and bill consumers accordingly.
With inelastic and stable demand and little threat of entry by new firms, the
existing four firms could earn substantial monopoly profits if they set prices
cooperatively. If, on the other hand, they compete aggressively, profits would fall
to nearly competitive levels.
The firms thus face a prisoners’ dilemma. Can cooperation prevail?
It can and has prevailed. There is rarely an attempt to undercut price, and each
firm appears satisfied with its share of the market. All four firms have been
earning returns on their investments that far exceed those in more competitive
industries.

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