Lecture 13: Coordination Problems

Today’s lecture was the last lecture. It was about coordination problems; matching players to achieve efficient outcomes. This is an area of incentive problems.

Multiple Payoff-equivalent Equilibria:
This is a kind of meet friend game(if they meet with each other in the same place, they will be happy otherwise, not. And the place is indifferent)
To attain coordination, we can use sequentially decision, communication, third-party recommendation, and convention.

Multiple Payoff-ranked Equilibria:
This is a kind of previous case, but one place is better than the other. In this case, pure strategy equilibria is same.

Payoff vs Risk(Stag hunt)
Consider previous game + Chicken(two same strategies’ pares are indifferent, and the others are only one player gets outcome).
There are two equilibriums. One is Pareto-dominant, the other is risk-dominant(because if one does not want to get Pareto-dominant equilibrium, one can make sure to get at least something slightly lower than Pareto-dominant equilibrium) there is two ways to attain coordination.
self-signaling:
action is an action chosen partly to secure good news about one’s traits or abilities, even when the action has no causal impact on these traits and abilities.
Self-commitment:
To show willingness to do something.

In this game, it is difficult to know what was perceived by other people.
Coordination on efficient outcomes is reached often with two-side communication, less often with one-sided communication, and very rarely without communication.

Without communication, if third party(public) suggestion is given, they can accept the suggestion if it is efficient equilibria, but otherwise, not.

Weak-Link Games:
Each player’s payoff is determined by the own choice and minimum of opponents’ choice.
For any number of players, there are 7 pure strategy equilibria(each player chooses same number in games)

Evidences:
By experiments, if number of player is increasing, the outcome become worse(because people think there are someone to choose 1).
Moreover, Increasing specialization(team size) can be dangerous. Raise team size only gradually, after having coordinated on a good outcome.

Organizational Languages:
Player: manager and workers
Rule: in 20 round, a manager teaches a worker a order of 8 of 16 pictures. And after that, half of workers join other managers’ pair and taught same thing as other workers do.

Result:
Over first 20 rounds, an efficient and relationship specific language develops (experienced workers are better than inexperienced)

It shows mergers lead to short-run loss of performance(of more than 25%), because of language mismatch.
We can say subjects overestimate value of mergers; they guessed that completion times would not decline so much.
Subjects attributed part of the decline to inefficient newcomers: workers rate new managers worse than old; managers rate new workers worse. Despite understanding that their task is harder (in this experiment, the work itself is same)

Multiple Efficient Equilibria;
“Battle of sexes”
(payoff matrix is like a chicken game, but two equilibriums are indifferent; one is good for one, another is good for another person), but if each of them choose same strategy, they get nothing.

In this game, one-side communication usually reach coordination.
Two-side communication, coordination achieved in 55% of cases if one round of communication; three round is 63%.
Without communication, coordination in 48% of cases.

Authority:
Formal authority: label(King, Boss)
Real authority is an equilibrium outcome

The label(boss, king) indicates that subordinates are supposed to play according to the authority’s directives, and to ignore competing massages from others(If players are given the role of king or servant, they can reach agreement easier than no role)

Remarks:
Labels only affect play if some convention(like the above) is attached.
A player has real authority if all others play the suggested equilibrium.
Formal authority is worthless absent real authority.
Authority only admits choice of equilibrium(do not affect strategy or payoff itself)

Absolute Authority:
The right a player can induce her preferred equilibrium.
If a player has absolute authority, efficient equilibrium is often not achieved because the player does not have credibility.

Divided Authority:
Magna Carta, and the Glorious Revolution gives king better position. Division of power can make everyone stronger by strengthening their commitment abilities.