Rational perspective to international negotiation are predicated on several basic ideas.

• Negotiators have a clear set of goals they want to accomplish. Negotiation is one of the options available to them in order to accomplish these goals.

• Negotiators are rational. Given a choice between or among several alternatives, they will choose that alternative that maximizes their expected utility. In other words, they will choose the alternative that has the highest possible prospect of accomplishing their goals.

Session #7:

• Each negotiator believes that the other side is also rational, and will choose that alternative which best serves its interests. So that if each side knows—or can guess—what are the interests of the other side, it can attempt to predict how the other side will behave in a given situation.

• In situation of negotiation, in general, and international negotiation, in particular, the negotiators are interdependent. This means that the result of each side’s decision depends on the decision of the other side.

• Each negotiator believes that the other side is also rational, and will choose that alternative which best serves its interests. So that if each side knows—or can guess—what are the interests of the other side, it can attempt to predict how the other side will behave in a given situation.

• In situation of negotiation, in general, and international negotiation, in particular, the negotiators are interdependent. This means that the result of each side’s decision depends on the decision of the other side.

• Rational choice theory can provide a normative benchmark for the analysis of negotiations. It can tell us for a given situation, if (a) the parties should negotiate, (b) if so what should they do during negotiation, and (c) if they do what they are supposed to do, what would be the “best possible”outcome.

• Very often, however, rational choice theory also attempts to be descriptive, that is, tell us what actually happens in the process of negotiation.

• Both last two ideas are controversial. We will criticize these ideas when we discuss psychological approaches to negotiation.

For now, however, we will rely on these ideas as the foundation for a rational choice analysis of negotiation

• Rational choice theory can provide a normative benchmark for the analysis of negotiations. It can tell us for a given situation, if (a) the parties should negotiate, (b) if so what should they do during negotiation, and (c) if they do what they are supposed to do, what would be the “best possible”outcome.

• Very often, however, rational choice theory also attempts to be descriptive, that is, tell us what actually happens in the process of negotiation.

• Both last two ideas are controversial. We will criticize these ideas when we discuss psychological approaches to negotiation.

For now, however, we will rely on these ideas as the foundation for a rational choice analysis of negotiation

• Understanding one’s goals, and being able to spell them out.

• Being able to prioritize goals.

• Being able to make tradeoffs among competing values.

• Being consistent, choosing according to the same principle every time and under all circumstances.

• Being able to incorporate uncertainty into the analysis and solution of problems

• Understanding one’s goals, and being able to spell them out.

• Being able to prioritize goals.

• Being able to make tradeoffs among competing values.

• Being consistent, choosing according to the same principle every time and under all circumstances.

• Being able to incorporate uncertainty into the analysis and solution of problems

What is a Game?

A “game” is a model of a given situation that contains four essential elements.

Actors: At least two players (players assumed to be rational utility maximizing entities). We distinguish between 2-person games and n-person games, with more than two players.

Alternatives: Each player has two or more courses of action (or inaction) at her disposal. We distinguish between simple (2 × 2) games and more complex games

What is a Game?

A “game” is a model of a given situation that contains four essential elements.

Actors: At least two players (players assumed to be rational utility maximizing entities). We distinguish between 2-person games and n-person games, with more than two players.

Alternatives: Each player has two or more courses of action (or inaction) at her disposal. We distinguish between simple (2 × 2) games and more complex games

The juxtaposition of the actors and their alternatives determines the outcome space of the game.

Preferences: a system for evaluating the outcomes of the game, from the point of view of the players’ goals. The outcomes of the game can be expressed either in terms of cardinal utility values real tangible values (e.g., money, size of territory, etc.), or they can be framed in terms of ordinal preference ordering.

Rules. A set of principles, typically not under the control of the players, that determines how the game is to be played. It covers such things as the sequence of play, the level of information available to players, the number of iterations, etc.

• By number of players: 2-person games versus n-person games

• By structure of preferences: constant (zero)-sum games, mixed-motive games, cooperative games.

• By types of rules: Single-play vs. iterative games, simultaneous vs. sequential choice games.

• By information structure: Full information vs. games with limited (incomplete) information

• By number of players: 2-person games versus n-person games

• By structure of preferences: constant (zero)-sum games, mixed-motive games, cooperative games.

• By types of rules: Single-play vs. iterative games, simultaneous vs. sequential choice games.

• By information structure: Full information vs. games with limited (incomplete) information

Row Player

Vote

Don’t Vote

Column Player

Vote Don’t Vote

John Wins with prob. 0.5

Sarah Wins with prob. 0.5

John Wins

Sarah Wins

John Wins with prob. 0.5

Sarah Wins with prob. 0.5

There are two voters (Row and Column) and two candidates: John and Sarah. Row prefers John, Column prefers Sarah. If there is a tie, it is broken by toss of a coin

Another way to represent this game

Row Player

Vote

Don’t Vote

Column PlayerVote Don’t Vote

1×0.5+(-1)×0.5=0

1, -1

-1, 1

1×0.5+(-1)×0.5=0

1×0.5+(-1)×0.5=0

1×0.5+(-1)×0.5=0

Assume that if one’s favorite candidate is elected the voter gets a utility score of 1, and if the other candidate is elected, the voter gets a score of -1.

A husband and wife discuss their plan to go out in the evening:

Husband: Wants to go to Ballet, does not want to go to the boxing match, but prefers going to the boxing match with his wife than going alone to the Ballet.

Wife: Prefers the boxing match over the Ballet, but would rather go to the Ballet with her husband than to the boxing match by herself.

Husband

Swan Lake

Boxing match

Wife

Swan Lake

Boxing Match

4, 3 2, 2

1, 1 3, 4

1 2 3 4 Husband’s utility

1

2

3

4

Wife’s utility

Husband—boxing; Wife--ballet

Husband—ballet; Wife--boxing

BATNA; mixed strategy solution

Both at the Ballet

Both at the boxing match Nash’s

bargaining solution

Nash’s bargaining solution

This idea really captures the basic conception of negotiations in game theory: it suggests that if both sides can do better by coordinating their behavior through some sort of agreement, then each side, and both collectively, can do better than the best each could do without an agreement.

This is the concept of Best Alternative to a Negotiated Agreement (BATNA). If each side can do better in an agreement than without it, then there is room for negotiations and both sides could agree on some level of coordination.

This idea really captures the basic conception of negotiations in game theory: it suggests that if both sides can do better by coordinating their behavior through some sort of agreement, then each side, and both collectively, can do better than the best each could do without an agreement.

This is the concept of Best Alternative to a Negotiated Agreement (BATNA). If each side can do better in an agreement than without it, then there is room for negotiations and both sides could agree on some level of coordination.

Row

Swerve

Don’t Swerve

Column

SwerveDon’t Swerve

C, C

3, 3

C, D

2, 4

D, C

4, 2

D, D

1, 1

Row

Col

umn

1

2

3

4

1 2 3 4

CC

CD

DC

DD

A Graphical Representation of the Game of Chicken

Row

Cooperate

Defect

Column

Cooperate Defect

3, 3 1, 4

4, 1 2, 2

Row

Col

umn

1

2

3

4

1 2 3 4

CC

CD

DC

DD

A Graphic Representation of the Prisoner’s Dilemma

An iterative Prisoner’s Dilemma (PD) was specified.

People were invited to write programs for playing the PD over a large number of iterations.

Each program was pitted against all other programs in a round-robin tournament, such that each program played each and every other program.

The winner was a simple strategy called Tit-for-Tat (TfT).

The TfT strategy is: cooperate on the first move, and emulate your opponent’s previous move thereafter

An iterative Prisoner’s Dilemma (PD) was specified.

People were invited to write programs for playing the PD over a large number of iterations.

Each program was pitted against all other programs in a round-robin tournament, such that each program played each and every other program.

The winner was a simple strategy called Tit-for-Tat (TfT).

The TfT strategy is: cooperate on the first move, and emulate your opponent’s previous move thereafter

First Generation 2nd Generation

3rd Generation 4th Generation

The Stag Hunt

4, 4

3, 1

1, 3Stag

Rabbit

Row

Column

2, 2

Stag Rabbit

Row

Col

umn

1

2

3

4

1 2 3 4

CC

CD

DC

DD