Genetic Algorithms, Learning, and the Dynamics of Corporate Takeovers

Thomas H. Noe
Department of Finance, Georgia State University and Federal Reserve Bank of Atlanta
TomNoe@gsu.edu

Lynn Pi
Deparment of Management and Finance, California State University-Hayward
balp626@academic.calpoly

Abstract

This paper simulates, via a genetic-learning algorithm, the problems of free-riding and coordination failure when shareholders are confronted with a tender offer bid between pre- and post-takeover firm value. Genetic algorithms simulate agent learning by assuming that each agent in a given strategic situation weighs only a finite number of possible strategies. His actual choice of response depends on which strategies have worked best in the past. However, the pool of strategies which are candidates for active implementation is not static over time. Agents ``learn", that is, they discard inferior strategies through a process called selection. Two selection processes are utilized in the simulations: one of these processes, termed ``utility-based" selection, specifies that the prevalence of a strategy in the updated gene pool be proportional to the payoff or ``utility" provided by the strategy in the previous round of the simulation. The second, more ordinal, ``rank-based" selection has the highest payoff strategies replace the lowest payoff strategies. Selection is augmented in two ways, though ``combining" old strategies, via a cross-over process, and by random adaption of totally new strategies, via strategic mutation. The strategy pool is used to determine the actual strategy played by each of the agents. These strategies, in turn, affect the payoff to other agents. Through the selection routine built into the genetic algorithm, this leads to a modification in the strategy pool used in the next round of play. To capture the effects of long-run learning, the process of game-playing and strategy-pool modification is iterated a number of times. Both the limits of the iteration process and the path of convergence are then investigated and compared with the outcomes predicted by the Nash equilibrium and the refinements of the Nash equilibrium.

The outcomes produced in the simulations offer qualified support for the hypothesis that coordination is impaired by increasing the number of shareholders. In no case do treatments featuring a large number of agents converge to the stochastically stable pure strategy limit points. Instead, they feature a significant randomization by agents and non-trivial probabilities of takeover failure. The results do not support the hypothesis of complete free-riding. Rather, the results support the hypothesis of partially successful coordination.

Moreover, the selection method utilized to update agent strategies has a significant impact on the outcome of the simulations. The strategy pools induced by the utility-based selection exhibit a small but consistent bias towards excessive tendering (relative to the predictions of Nash equilibria). The increase in the total gains induced by this bias towards overtendering more than offsets the potential losses from randomization-induced coordination failures. Thus, the probability of takeover success, though reduced, remains high even when the number of shareholders is fairly large. Interestingly, the same over-tendering phenomenon in unconditional tender offers has been observed in human-subject takeover experiments (Kale and Noe, 1994) and in closely related public-goods experiments (Palfrey and Rosenthal, 1991).

On the other hand, rank-based selection yields a fraction of shares tendered which conforms closely with fractions induced by Nash equilibria. Moreover, in the simulations featuring a large number of shareholders (more than fifty) the relationship between raider and shareholder profit produced by the rank-based simulations almost perfectly conforms with the relationship obtaining in the Nash equilibria of tender offer games featuring a large number of shareholders. Finally, because the rank-based treatments lack the upward bias in tendering probabilities observed in the utility-based treatments and in human-subject experiments, and they feature limiting strategy distributions exhibiting considerable randomization, they produce high probabilities of tender offer failure when the number of shareholders is large.

In addition yielding results supporting the intuitive, but difficult to formally justify, notion that increasing the number of agents increases coordination problems, the simulation results, at least those utilizing utility-based selection, provide partial support for the idea developed in Holstrom and Nalebuff (1992) that increasing the divisibilty of shareholding increases the probability of takeover success. As divisibility of holding increases, the tendering distribution tends to concentrate on intermediate fractions of shareholdings. This effect is observed under both utility- based and rank-based selection. However, only when utility-based selection is employed, is it strong enough to engender a significant increase in success probabilities and shareholder profits.

Thus, the genetic learning algorithm captures a number of aspects of agent behavior which are not predicted by the Nash solution concept or its learning or coordination-based refinements. These include an increased tendency of takeover bids to fail with increases in the number of shareholders, the tendency of agents to ``overtender," the ability of share divisibility to reduce the degree of randomization in tendering patterns. The fact that all of these aspects of agent behavior seem quite commonsensical and/or are supported by experimental evidence, yet none of them follows from formal analysis which ignores bounded rationality, leads one tentatively to the conclusion that implicit appeals to computational and/or information-processing limitations of agents underlies much of the folk wisdom surrounding the discussion of strategic behavior. More importantly, such considerations of the neurocomputational limitations or rational actions may play an important part in the formulation of behaviorally realistic models of ecnonomic behavior.