sequential+move+games

Jeff Butcher Rebecca Yagelski

Sequential move games, also called multistage games, are games in which there is a strict order of play. In simplest terms, this could refer to a game of checkers, tic-tac-toe, or chess. Players in a sequential move game use all of the information regarding what has happened so far in the game in order to formulate their next decision. As a result, strategy comes into play both for the player acting first and the player acting second.

There are several things that make sequential move games more complicated in real life. One of these is lack of information; players often don't know the actual payoffs to other players. Therefore, players should research their opponent before starting the bargaining process. An example would be an individual who wants to purchase farmland. If the buyer doesn't know what the seller's cost of the land is, then it complicates the bargaining process. With this lack of knowledge, the buyer can't make a take-it-or-leave-it offer and be confident that he/she will get the land. However, the buyer could do research to learn the current asking prices or recent selling prices for comparable land in the area to assist with the bargaining process. There is an assumption in the literature that is made in the bargaining process that the game ends once the second player rejects/accepts an offer. However, this is not always the case in reality which changes the dynamics of the game. Whether or not the players are actually making a take-it-or-leave-it offer and how the other players perceive the offer make the bargaining process more complicated. For example, a buyer might reject a sellers offer of $500 for a computer hoping that the seller will make a counteroffer that is better (i.e. $400).

Sequential move games are most easily represented and explained in extensive form. Extensive form refers to a representation of the game that summarizes, who, when, what and how much and is best shown using a decision tree. When using a decision tree, the circles are referred to as decision nodes and indicate that at that particular point in the game a player, depicted in the node, must make a decision. The point at which all of the lines originate is the beginning of the game. The numbers to the right of the decision tree indicate the payoffs for each of the respective decisions made by the players.

Example:

There are two firms – G and B. Each firm’s decision to advertise or not advertise affects the amount of profit made. When both firms advertise their profits are $3. When both firms don’t advertise their profits are $10. When one firm advertises and the other does not, the advertising firm receives $4 in profit and the non-advertising firm receives $6 in profit. In this game, firm G gets to decide first. The decision tree for this game can be found through the link below. (NA refers to No Advertising and A refers to a decision to advertise)



Test Questions:

1. Does a nash equilibruim exist in the example above? a. Yes b. No c. not enough information

2. In the example above, if a Nash Equilibrium does exist, what is it? a. both firms advertise b. both firms don't advertise c. firm G advertise and firm B does not d. Nash Equilibrium does not exist

3. Players in sequential move games should always assume that the bargaining process is finished once the second player rejects/accepts an offer? a. True b. False

4. Which of the following is __not__ an aspect of sequential move games? a. There is a strict order of play b. Players use all of the information (regarding what has happened so far in the game) to make their next decision c. The outcome of the game would not change regardless of the order of play (who gets to go first) d. Players don't always know the payoffs to other players

Answers: 1. a 2. b 3. b 4. c

Source: Managerial Economics and Business Strategy, by Michael Baye Lecture notes: http://www.pitt.edu/~jduffy/econ1200/LectNotesWk2_Handouts.pdf