By Chris Badger

When you hear the word strategic planning, two images come to mind—war and games. In a game, individual players must plan their own moves, anticipating the possible moves both they and their opponents can make in order to win. Game theory is a psychological and economic theory used to evaluate and predict behavioral tendencies—individual “players” are confronted with various market “games” that require strategic planning to “win.” As in any game, there is a predetermined set of moves that players can make in the game. To “win”, a player needs to know and anticipate for every move that they, and the other players, could possibly make.

The best players of any game not only need to analyze what their best next move will be, but also attempt to analyze their opponent’s next best moves. Game theory has real-world analogues in finance, and we will explore its application in mergers and acquisitions.

The Prisoners’ Dilemma
The most widely used application of game theory is “The Prisoners’ Dilemma.” This “game” begins with two accused bank robbers. The police officers responsible for their case decide that the most effective way to gain confession is to separate the suspects into two different rooms, and make them each an offer to incentivize betraying the other. This offer is simple: if neither suspect confesses, neither will be imprisoned; if only one of the suspects confesses, the confessor will receive 2 years in prison while their comrade, who remained silent, will get 15 years; if both suspects confess, both prisoners be sentenced to 5 years in prison.

It’s obvious that the best outcome results when both suspects stay silent. However, we all know there is no honor among thieves. As individuals are rational actors, both robbers will realize that the best thing for them is to confess. While they won’t go home free, they are both guaranteed a lower jail sentence in the event the other suspect confesses as well—it’s better to serve 5 years (both confess) than 15 (I stay silent while I’m betrayed).

Partners in a firm about to be acquired are in a similar position to the suspects in the Prisoners’ Dilemma, without the criminal implications, of course. Rather than deciding whether or not to confess to a crime, partners must decide whether or not to stay with the firm. This decision has implications for both the buyer and the seller: both parties can use game theory to their advantage.

Application of Game Theory
Let’s apply the Prisoner’s dilemma to a game of acquisition. Just like our bank robbers, there is an optimal result when all “players” cooperate and work together; however, rational actors will always act in their own best interest, even if it results in a sub-optimal outcome for the game.

The optimal result for the acquiring company occurs when all partners in the acquired firm decide to stay. Therefore, the acquiring company will be incentivized to retain the partners by ensuring that the offered benefit to remain is greater than any external offers from competing firms. However, partners are also aware that it is in the acquiring firms’ best interest for them to stay. Partners will therefore leverage external offers from other companies in order to increase the offer from the acquiring company to retain their loyalty.

Without original company structure, there is no guarantee that the acquiree will remain successful—the acquisition could still go through but fail to make a return on investment. Partners leaving the firm could also result in the acquisition coming to a standstill, leaving the acquiree without a buyer. Often, the premature end of the acquisition process equates to decreased sales and returns at both firms involved, and a poor image of the would-be acquirer in the market.

The Partners’ Dilemma
We can use basic game theory to avoid suboptimal results. The firm’s partners have a few things to consider when deciding whether to leave the company. As partners leave, other job opportunities at that high level are going to go to the partners who leave the earliest, due to shortage in demand. To keep an equivalent position, a partner would either have to be one of the first to defect or stay on with the firm. The partners know that it is not in their best interest to stay while others defect, and so rationally, will try to be the first to leave.

Knowing that the partners will seek to leave, the acquiring firm will understand that in order to keep the partners and create the optimal acquisition, they must incentivize loyalty by offering a greater benefit to the partners than any that they could gain from defection.

Ultimately, both the acquirer and the acquiree in any given acquisition are using game theory to anticipate the other’s moves and motivation. The key is to understand this “game” and know the options that all the players have to choose from. Knowing the best options for not only yourself, but for all the players in the game will allow you to anticipate needs and mitigate against threats to create the optimal result for you and your firm.

About Chris Badger
Chris Badger is a Partner at NOW CFO with experience in strategic management, external financial reporting, board relations and investor relationships. He holds a BA in Accounting from the University of Utah and an MBA from Keller Graduate School of Business. Chris is also a licensed CPA.