Game theory applications in finance

The two most important solution techniques for games with simultaneous moves are Nash equilibrium analysis and dominance. Only pure equilibrium strategies, i. A more powerful method in determining the outcome of a simultaneous move game is dominance. The strategies eliminated with this concept are called dominated strategies. From this argument it is obvious that the solution is very powerful: each player has clear incentives to play the dominant strategy if there is one.

When moving from simultaneous move to sequential move games, the thinking involved in finding equilibria changes: given the chronological differences, solutions are found by looking ahead and reasoning back. This is done by examining the end of the game and determining which actions the last player will choose equivalent to which ones will not be chosen. Reasoning back to the second-to-the-last player and determining the best strategy, given the choices of the last player, starts a series called rollback reasoning.

It is used at each node until the initial node is reached and is therefore called rollback or backward induction ; the outcome is known as rollback equilibrium. One assumption underlying the equilibrium analysis described in the previous chapter is that of complete information about all moves, outcomes and probabilities, i.

This chapter explores the concepts game theory offers to address situations with asymmetric information, i. There are two situations considered in the literature: imperfect and incomplete information. Imperfect information means that at least one player by the time of at least one action in the game does not know what outcome an action by a preceding player had brought about.

The two most important strategic concepts used in games with adverse selections are signaling and screening. Nevertheless, not taking a signaling action is already a signal to the uninformed player, who can conclude that the information is not advantageous.

A field also based on issues of asymmetric information is the literature on agency conflicts, which can be interpreted as the game theoretic study of certain contractual structures under asymmetric information.

The theory models contractual structures where a worse informed principal wants to induce a better informed agent to act in its interest. The literature on signaling [45] and agency theory opened financial economics to the analytic tools of game theory. Suddenly, strategic behavior and information played a crucial role in determining important financial issues, such as dividend and capital structure policy. However, according to Thakor the early signaling models were not game-theoretic models in a strict sense.

Granted, they used some game theoretic concepts as they implicitly studied games with strategic interactions among several players. On the other hand, they did not explicitly specify a formal structure for those games.

This is a problem from a game theoretic standpoint, as concepts like Nash equilibrium require a specification of the outcomes off the equilibrium path of the game. If it is ex ante efficient for the informed player to emit a certain signal according to his type, this is the signaling equilibrium. Nevertheless, it is a necessary condition for an equilibrium that abiding by this signal e. Rigorous game theoretic modeling provides analytic tools to overcome those difficulties implicit in the first models of asymmetric information.

Such implicit inaccuracies are averted by explicitly specifying the studied game in extensive form and reversing the order of moves, as Thakor demonstrated with the Ross incentive signaling model. Reversing the order of moves means that the informed player is assumed to move first by signaling based on his private information.

Explicitly game-theoretic signaling models also have the advantage that everything is made precise: the sequence of moves, possible off-equilibrium paths and reactions etc. This eliminates any ad hoc solutions, providing an extensive analysis that does not encounter the problems inherent in earlier signaling models. However, those models have provided important insights into the implications of asymmetric information for finance.

Therefore, it is important to describe them, as well as recent, more rigorous game-theoretic treatments of financial issues. One of the most extensively researched issues in finance has been what Black termed the dividend puzzle. To this day substantial progress has been made in researching the tax effects and the information effects of dividends.

The empirical evidence on tax effects is mixed and inconclusive [56] , but the signaling literature focusing on the information contained in the announcement of dividends has produced important insights. MM already suggested in their original paper that dividends might convey important information about a firm's prospects, but it was not until 20 years later that initial attempts were undertaken to understand this issue.

By committing to a high level of dividends, they can signal this to the market, which rewards the firm with a higher valuation. The first problem arises when the total risk capital withheld by a firm needs to be divided over several business divisions within the firm.

The second problem deals with a business sector, where it is determined how companies compensate customers of bankrupted competitors for their losses. The aforementioned problems are not only studied by construction cooperative games, but by applying the underlying rationale to the specific problems as well.

AB - In finance, situations exist that give rise to allocation problems. Overview Fingerprint. Abstract In finance, situations exist that give rise to allocation problems. 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.

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.