Gaming and Strategic Decisions

First, we should clarify what gaming and strategic decision making are all about. A game is any situation in which players (the partici­pants) make strategic decisions—i.e., decisions that take into account each other’s actions and responses. Examples of games include firms competing with each other by setting prices, or a group of consumers bidding against each other at an auction for a work of art. Strategic decisions result in payoffs to the players: outcomes that generate rewards or benefits. For the price-setting firms, the payoffs are profits; for the bidders at the auction, the winner’s payoff is her consumer surplus—i.e., the value she places on the artwork less the amount she must pay.

A key objective of game theory is to determine the optimal strategy for each player. A strategy is a rule or plan of action for playing the game. For our price­setting firms, a strategy might be: “I’ll keep my price high as long as my com­petitors do the same, but once a competitor lowers his price, I’ll lower mine even more.” For a bidder at an auction, a strategy might be: “I’ll make a first bid of $2000 to convince the other bidders that I’m serious about winning, but I’ll drop out if other bidders push the price above $5000.” The optimal strategy for a player is the one that maximizes the expected payoff.

We will focus on games involving players who are rational, in the sense that they think through the consequences of their actions. In essence, we are con­cerned with the following question: 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? In real life, of course, you may encounter competi­tors who are irrational, or are less capable than you of thinking through the consequences of their actions. Nonetheless, a good place to start is by assuming that your competitors are just as rational and just as smart as you are.¹ As we will see, taking competitors’ behavior into account is not as simple as it might seem. Determining optimal strategies can be difficult, even under conditions of complete symmetry and perfect information (i.e., my competitors and I have the same cost structure and are fully informed about each others’ costs, about demand, etc.). Moreover, we will be concerned with more complex situations in which firms face different costs, different types of information, and various degrees and forms of competitive “advantage” and “disadvantage.”

Noncooperative versus Cooperative Games

The economic games that firms play can be either cooperative or noncooperative. In a cooperative game, players can negotiate binding contracts that allow them to plan joint strategies. In a noncooperative game, negotiation and enforcement of binding contracts are not possible.

An example of a cooperative game is the bargaining between a buyer and a seller over the price of a rug. If the rug costs $100 to produce and the buyer values the rug at $200, a cooperative solution to the game is possible: An agree­ment to sell the rug at any price between $101 and $199 will maximize the sum of the buyer’s consumer surplus and the seller’s profit, while making both par­ties better off. Another cooperative game would involve two firms negotiating a joint investment to develop a new technology (assuming that neither firm would have enough know-how to succeed on its own). If the firms can sign a binding contract to divide the profits from their joint investment, a cooperative outcome that makes both parties better off is possible.

An example of a noncooperative game is a situation in which two compet­ing firms take each other’s likely behavior into account when independently setting their prices. Each firm knows that by undercutting its competitor, it can capture more market share. But it also knows that in doing so, it risks setting off a price war. Another noncooperative game is the auction mentioned above: Each bidder must take the likely behavior of the other bidders into account when determining an optimal bidding strategy.

Note that the fundamental difference between cooperative and noncoop­erative games lies in the contracting possibilities. In cooperative games, binding contracts are possible; in noncooperative games, they are not.

We will be concerned mostly with noncooperative games. Whatever the game, however, keep in mind the following key point about strategic decision making:

This point may seem obvious—of course, one must understand an opponent’s point of view. Yet even in simple gaming situations, people often ignore or misjudge opponents’ positions and the rational responses that those positions imply.

HOW TO BUY A DOLLAR BILL Consider the following game devised by Martin Shubik. A dollar bill is auctioned, but in an unusual way. The highest bidder receives the dollar in return for the amount bid. However, the second- highest bidder must also hand over the amount that he or she bid—and get nothing in return. If you were playing this game, how much would you bid for the dollar bill?

Classroom experience shows that students often end up bidding more than a dollar for the dollar. In a typical scenario, one player bids 20 cents and another 30 cents. The lower bidder now stands to lose 20 cents but figures he can earn a dollar by raising his bid, and so bids 40 cents. The escalation continues until two players carry the bidding to a dollar against 90 cents. Now the 90-cent bidder has to choose between bidding $1.10 for the dollar or paying 90 cents to get nothing. Most often, he raises his bid, and the bidding escalates further. In some experi­ments, the “winning” bidder has ended up paying more than $3 for the dollar!

How could intelligent students put themselves in this position? By failing to think through the likely response of the other players and the sequence of events it implies.

In the rest of this chapter, we will examine simple games that involve pricing, advertising, and investment decisions. The games are simple in that, given some behavioral assumptions, we can determine the best strategy for each firm. But even for these simple games, we will find that the cor­rect behavioral assumptions are not always easy to make. Often they will depend on how the game is played (e.g., how long the firms stay in business, their reputations, etc.). Therefore, when reading this chapter, you should try to understand the basic issues involved in making strategic decisions. You should also keep in mind the importance of carefully assessing your opponent’s position and rational response to your actions, as Example 13.1 illustrates.

Source: Pindyck Robert, Rubinfeld Daniel (2012), Microeconomics, Pearson, 8th edition.