In sequential games, a series of decisions are made, the outcome of each of which affects successive possibilities. In game theory, the analysis of sequential games is of great interest because they usually model reality better than simultaneous games: producers will usually observe demand before deciding how much output to produce, duopolists will observe each other’s decisions before dumping more goods in the market, etc. For example, let’s examine the decision a company faces when trying to break a market which is currently a monopoly. Sequential games are represented through decision trees, with successive nodes at each decision point:
The game represented in this decision tree shows firm 1 choosing whether to compete in a monopolistic market or not. As there are no existing competitors in the market, should they choose not to enter, its payoff will be zero and the existing monopoly will have a payoff of two. However, if firm 1 chooses to enter we reach node two, where the second decision must be made by the challenged player (the monopoly), whether to accommodate the new competitor or fight back to try and block its entry. In this particular example, if they choose to fight, both players will have a payoff of -1, whereas if the monopoly decides to accommodate the new player, our monopoly becomes a duopoly and the resulting drop in prices creates larger market demand, meaning that the existing company will still receive a payoff of one and the new player a payoff of two.
So, what can we assume will happen? We assume that both players dispose of complete and perfect information. They have both carried out a thorough market study and know the consequences of each outcome. In that case, what they can do is work backwards to know what the competition will do. If firm 1 enters the market, player 2 has no reason to fight back, as its payoff will suffer by two points. This means that player 2 knows what the outcome will be if they choose to enter, so all they have to do is choose between a payoff of two if the new firm enters the market or zero if it doesn’t. In this case, it is pretty clear what the outcome will be. The game would change again, of course, if successive nodes were introduced, where fighting could again flip the tables.