11 Pages Posted: 23 Jun 2009
The note begins by suggesting various dimensions along which competitive situations may differ. It then introduces the matrix game structure and means to analyze a matrix games through iterative domination. The terms, Pareto-optimal and equilibrium are introduced. The note ends with a review of several classical matrix game structures: No Conflict Dilemma and Battle of the Sexes.
Rev. Jan. 25, 2011
Key sources of uncertainty in many decisions are the actions that others may take in response to or in preemption of the actions that we take. The proactive decision maker can describe these uncertain behaviors with the same probability language that is used to describe the uncertainty arising from imperfect knowledge of the physical or economic environments around us. But, because the actions of others are driven by their interests and by their economics, the probability assessment process should be informed by a careful consideration of the forces that motivate those actions. It would be myopic and naive to pretend that the actions of others are simply random and not the result of mindful thought and analysis. In addition to making an informed assessment about the actions of others, the proactive decision maker should explicitly consider the options and motivations of others in an effort to create new alternatives that might guide the behaviors of others and/or that might be more attractive to all parties involved. This note provides a framework for explicitly considering the interactions between our actions and the actions of others who may be directly or indirectly involved in the situation.
Throughout the discussion that follows, the other parties will be referred to as competitors and the situation will be described as competitive. Although this is the common context in which the interactions addressed in this note arise, the broader perspective of interested party should be kept in mind. An interested party may be a competitor, but might also be a colleague, a partner, a government agency, or a special interest group. The critical characteristic of these competitive situations is that the performance of our alternatives is impacted by the actions of the competitors. This does not necessarily mean that our interests will be in conflict with those of others, as the word competitor might suggest, but just that our performance is linked to their actions.
This note begins by presenting a variety of characteristics that can be used to frame different competitive situations and to better understand the potential implications of the competitive interaction. In the second section, the format of matrix games is introduced as a means to succinctly present the alternatives available to the parties involved and the mutual consequences of all the potential combinations of actions. The note ends with a description of three classical competitive situations (no conflict, prisoner's dilemma, and preemption) and the managerial messages associated with each.
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Keywords: game theory, matrix organization
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