Coordination Games

Definition:
A game in which the players benefit from working together is a coordination game. When participants work together for the benefit of all, the solutions to problems are cooperative solutions. The challenge in a cooperative game is for each individual participant to determine what course of action will provide the most benefit to all of the participants in the game. That course of action, in turn, will also provide the most benefit for each individual participant. In a coordination game, there is no incentive for either party to cheat since it will result in a worse outcome than cooperating. Coordination games that adhere to a 2 x 2 normal form have exactly 2 Nash equilibria.

Examples:
An example of how organizations can collaborate to serve all of their collective interests comes from Brandenburger and Nalebuff. The authors describe how teams in the National Football League control the supply of teams to negotiate with cities and fans in order to obtain the best deal for themselves. With a limited number of teams in the NFL, the owners are ensured that there will always be fewer teams in the league than there are cities (and their fans) who are willing to pay to try to lure a team. When the St. Louis Cardinals moved to Phoenix in 1988, the city of St. Louis was stuck with a football stadium but no team to play its home games inside. This situation provided the city of St. Louis an incentive to try to lure an NFL franchise to the city, but it took some time before it was able to do so. In the interim period before St. Louis was finally able to attract the Rams from Los Angeles, the generous offers made by the city of St. Louis were matched by cities with existing teams that weren’t interested in their team moving to St. Louis. When the Rams did move to St. Louis, they left behind an empty stadium in Los Angeles.

Roger McCain provides an excellent and important example that demonstrates the importance of cooperation in every day life in his book “Game Theory: A Non-Technical Introduction to the Analysis of Strategy.” Consider that two cars are driving down the road and will soon meet each other. One of the cars is a Mercedes (M) and the other is a Buick (B). Each car can choose to drive on the left side of the road (L) or the right side of the road (R). In the United States, of course, each car would drive on the right side of the road and the two cars would not collide. But what if the two cars didn’t have the guidance of this simple traffic regulation? Let’s say that if the two cars pass each other without incident, they each score a 1 and that a collision results in a score of -10 for both cars. McCain provides a chart to show the possible outcomes of this situation:



Mercedes



Left
Right
Buick
Left
1, 1
-10, -10

Right
-10, -10
1, 1

It’s easy to see why it’s so important for the drivers of the two cars to coordinate so that they each drive on the same side of the road to avoid a collision. Naturally, in the United States both drivers would drive on the right side and in Britain they would both drive on the left side and these social guidelines would lead to safe travel for both cars. It’s also interesting to note that neither driver would benefit from ignoring the regulations of the road and trying to “steal” another car’s rightful lane, since this would lead to a collision that would harm both drivers. In a coordination game like this, one’s own self interest is served by following the rules. When a person makes a choice out of self interest, it simultaneously serves the interest of another individual.

The conventional perception of coordination games is that both parties benefit by choosing the same outcome as demonstrated in the example above. With a pure asymmetic coordination game, both parties benefit by choosing different outcomes. An example of such a coordination game is when two people are talking on the phone and their call is disconnected. If the first and second person immediately redial or wait for the other person to call, they will not be reconnected. It is only when one party waits and the other party redials that the call is reconnected. The table below illustrates this example (Wang & Yang, 2003).



Party B



Wait
Redial
Party A
Wait
0,0
10,10

Redial
10,10
0,0


References:
Brandenburger, Adam M. and Nalebuff, Barry J. Co-opetition. May 1996. pp. 43-44.

McCain, Roger. Game Theory: A Non-Technical Introduction to the Analysis of Strategy. 2003
http://william-king.www.drexel.edu/top/eco/game/multnash.html

Wang, X.H. & Yang, B.Z. "Classification of 2x2 games and strategic business behavior," The American Economist, 47(2): 78-85, 2003.

Sample Test Questions:
1. A new baseball league is being formed with four teams all located about 50 miles from each other in the same state. The general manager of one of the teams is trying to decide what amount of money should be charged for each ticket given that the stadium is small and every seat provides a very similar view of the game. The GM also knows that the other three teams in the league are charging $5 for each ticket and must price tickets keeping in mind that for each game, the visiting team will share the proceeds from ticket sales. What price should be charged for each ticket?

a. $10
b. $7
c. $3
d. $5

Answer: The general manager should charge $5 for a single game ticket. She may be tempted to charge less than $5 in an attempt to draw more fans to each game and perhaps lure fans from some of the other cities in the league. However, luring fans away from the other teams is not a good strategy, because it would decrease the amount of revenue shared with the team that will be received when the team plays road games as a visitor in the other stadiums on the league.

2. Two new businesses have opened in an area where they share a parking lot. Space is limited directly in front of the two businesses, so they have posted a sign restricting the use of the parking spaces to patrons of one of the two businesses. What is the best way for the businesses to make sure that the parking spots are only used by their patrons?
a. Pay an employee to follow anyone who parks in one of the spaces to see if that person enters one of the new businesses
b. Buy a tow truck and park it right in the middle of the two businesses
c. Trust that the sign alone is enough to deter non-patrons from using the parking spaces without any actual enforcement
d. Work together to share the cost of cameras and software that will monitor the use of the parking spots and request the tow of a car even if it is parked in front of the other business and not one's own business

Answer: These two businesses should work together to enforce the protect the most desirable parking spots in front of their respective businesses.

3. A single gas station opens in a small town and must decide between offering regular gas or ethanol. At the same time, a resident of the town is trying to decide whether to buy a car that runs on regular gas or ethanol. The normal-form game is shown below.



Gas Station



Regular Gas
Ethanol
Car buyer
Regular Gas
10, 10
0, 0

Ethanol
0, 0
10, 10

This game is known as:
a. Bertrand duopoly game
b. Nash bargaining game
c. extensive-form game
d. coordination game

Answer: d) coordination game

4. In the preceding example, how many Nash equilibria are present?

a. zero
b. one
c. two
d. three

Answer: c) two

5. True of False: In a coordination game such as the example in question 3, it is easier for both parties to obtain a favorable outcome in a simultaneous-move game.

Answer: False. It is easier for the parties to obtain a favorable outcome in a sequential-move game.