Browsing by Subject "Game Theory"

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    Game-theoretic models for mergers and acquisitions
    (1995) Van den Honert, Robin Charles; Stewart, Theodor J
    This thesis examines the corporate merger process as a bargaining game, under the assumption that the two companies are essentially in conflict over the single issue of the price to be offered by the acquirer to the target. The first part of the thesis deals with the construction and testing of analytical game-theoretic models to explain the proportion of the synergy gains accruing to the target company under different assumptions about the players' a priori knowledge. Assuming full certainty amongst the players about the pre- and post-merger values of the companies, the distribution of gains between target and acquiring companies that would be consistent with the Nash-Kalai axioms is determined in principle. The resulting model depends on the players' utility functions, and is parameterised by the relative bargaining strength of the players and their risk aversion coefficients. An operational version of the model is fitted to empirical data from a set of 24 recent mergers of companies quoted on the Johannesburg Stock Exchange. The model is shown to have good predictive power within this data set. Under the more realistic assumption of shared uncertainty amongst the two players about the post-merger value of the combined company, a Nash-Kalai bargaining model incorporating this uncertainty is developed. This model is an improvement over those with complete certainty in that it offers improved model fit in terms of predicting the total amount paid by an acquirer, and is able to dichotomise this payment into a cash amount and a share transfer amount. The theoretical model produced some results of practical value. Firstly, a cash-only offer is never optimal. Conditions under which shares only should be tendered are identified. Secondly, the optimal offer amount depends on the form of payment and the level of perceived risk. In a share-only offer the amount is constant regardless of risk, whilst if cash is included an increase in risk will imply a decrease in the optimal amount of cash offered. The Nash-Kalai model incorporating shared uncertainty is empirically tested on the same data set used previously. This allows a comparison with earlier results and estimation of the extent of the uncertainty. An extension of this model is proposed, incorporating an alternative form of the utility functions. The second part of the thesis makes use of ideas from negotiation analysis to construct a dynamic model of the complex processes involved in negotiation. It offers prescriptive advice to one of the players on likely Pareto-optimal bargaining strategies, given a description of the strategy the other party is likely to employ. The model describes the negotiating environment and each player's negotiating strategy in terms of a few simple parameters. The model is implemented via a Monte Carlo simulation procedure, which produces expected gains to each player and average transaction values for a wide range of each of the players' strategies. The resulting two-person game bimatrix is analysed to offer general insights into negotiated outcomes, and using conventional game-theoretic and Bayesian approaches to identify "optimal" strategies for each of the players. It is shown that for the purposes of identifying optimal negotiating strategies, the players strategies (described by parameters which are continuous in nature) can be adequately approximated by a sparse grid of discrete strategies, providing that these discrete strategies are chosen so as to achieve an even spread across the set of continuous strategies. A sensitivity analysis on the contextual parameters shows that the optimal strategy pair is very robust to changes to the negotiating environment, and any such changes that have the players start negotiating from positions more removed from one another is more detrimental to the target. A conceptual decision support system which uses the model and simulated results as key components is proposed and outlined.
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    Open Access
    Purely competitive evolutionary dynamics for games
    (2012) Veller, Carl; Rajpaul, Vinesh
    We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial, are governed. In each period, the population is randomly sorted into pairs, which engage in a once-off play of the game; the probability that a member propagates its type to its offspring is proportional only to its payoff within the pair. We show that if a type is dominant (obtains higher payoffs in games with both other types), its 'pure' population state, comprising only members of that type, is globally attracting. If there is no dominant type, there is an unstable 'mixed' fixed point; the population state eventually oscillates between the three near-pure states. We then allow for mutations, where offspring have a non-zero probability of randomly changing their type. In this case, the existence of a dominant type renders a point near its pure state globally attracting. If no dominant type exists, a supercritical Hopf bifurcation occurs at the unique mixed fixed point, and above a critical (typically low) mutation rate, this fixed point becomes globally attracting: the implication is that even very low mutation rates can stabilize a system that would, in the absence of mutations, be unstable.