10.3: Repeated and Sequential Games

Repeated Games

A game that is played only once is called a “one-shot” game. Repeated games are games that are played over and over again.

Repeated Game = A game in which actions are taken and payoffs received over and over again.

Many oligopolists and real-life relationships can be characterized as a repeated game. Strategies in a repeated game are often more complex than strategies in a one-shot game, as the players need to be concerned about the reactions and potential retaliations of other players. As such, the players in repeated games are likely to choose cooperative or “win-win” strategies more often than in one shot games. Examples include concealed carry gun permits: are you more likely to start a fight in a no-gun establishment, or one that allows concealed carry guns? Franchises such as McDonalds were established to allow consumers to get a common product and consistent quality at locations new to them. This allows consumers to choose a product that they know will be the same, given the repeated game nature of the decision to purchase meals at McDonalds.

Sequential Games

A sequential game is played in “turns,” or “rounds” like chess or checkers, where each player takes a turn.

Sequential Game = A game in which players move in turns, responding to each others’ actions and reactions.

Product Choice Game One

An example of a sequential game is the product choice game shown in Figure \(\PageIndex{1}\).

In this game, two cereal producers (Kelloggs and General Mills) decide whether to produce and sell cereal made from wheat or oats. If both firms select the same category, both firms lose five million USD, since they have flooded the market with too much cereal. However, the two firms split the two markets, with one firm producing wheat cereal and the other firm producing oat cereal, both firms earn ten million USD. In this situation, it helps both firms if they can decide which firm goes first, to signal to the other firm. It does not matter which firm produces wheat or oat cereal, as long as the two firms divide the two markets. This type of repeated game can be solved by one firm going first, or signaling to the other firm which product it will produce, and letting the other firm take the other market.

Product Choice Game Two

It might be that one of the two markets is more valuable than the other. This situation is shown in Figure \(\PageIndex{2}\).

This cereal market game is very similar to the previous game, but in this case the oat cereal market is worth much more than the wheat cereal market. As in the Product Choice One game, if both firms select the same market, both lose five million USD. Similarly, if each firm chooses a different market, then both firms make positive economic profits. The difference between the two product choice games is that the earnings are asymmetrical in the Product Choice Two game (Figure \(\PageIndex{2}\)): the firm that is in the oat cereal market earns 20 million USD, and the firm in the wheat cereal market earns 10 million USD. In this situation, both firms will want to choose OAT first. If Kelloggs is able to choose OAT first, then it is in General Mill’s best interest to select WHEAT. The player in this sequential game who goes first has a first player advantage, worth ten million USD. Each firm would be willing to pay up to ten million USD for the right to select first. In a repeated game, the market stabilizes with one firm producing oat cereal, and the other firm producing wheat cereal. There is no advantage for either firm to switch strategies, unless the firm can play OAT first, causing the other firm to move into wheat cereal.