A Brief Overview of Game Theory, Operations Research, and Their Roles in Better Decision-Making

Çağlar Çağlayan

by
Research Associate, Robert H. Smith School of Business, University of Maryland College Park

The topic of this issue of OR/MS Tomorrow is about Game Theory and Operations Research. Accordingly, we want to give a brief overview of these two fields, introduce their fundamental concepts, and discuss their roles in better decision-making.   

Operations Research (OR) is the scientific study of the management of operations and processes for the purpose of better problem-solving and decision-making (Horner, 2015). Using the tools of mathematics, statistics and computer science, OR researchers and practitioners are concerned with how managerial decisions that control the operations of the system of interest should be made and implemented to improve the targeted outcome(s) (Tanenbaum & Eilon, 2018).  Some of the basic concepts of OR are as follows:

  • Model: The conceptual representation (and the mathematical formulation) of the real-life problem of interest to be simulated or mathematically solved.
  • Optimization: Among all feasible alternatives, finding the solution with the highest achievable performance under given constraints and resources.
  • Decision Variables: The actions/quantities to be determined from a given (possibly unbounded) set of feasible alternatives.
  • Objective Function: The targeted outcome(s) to be optimized (i.e., maximized or minimized) by controlling the decision variables.
  • Constraints: The equalities and inequalities that mathematically represents characteristics and the real-life limitations of the problem of interest.
  • Feasible Solution: A specific value of decision variables satisfying all constraints.
  • Process: The description of how the system of interest behaves/evolves, which is mathematically represented via constraints and decision variables. A process is considered “deterministic” when all parameters of the constraints are (assumed to be) known with certainty, and “stochastic” if it is inherently probabilistic and its probabilistic features are captured in the mathematical model.

Game Theory (GT) is the mathematical study of strategies, cooperation and situations involving conflicting interests, in which an agent’s success in making choices (and achieving her desired outcome) depends on the choice(s) of other decision-maker(s) (Bhuiyan, 2018). It serves as a formal framework for describing social and business interactions and analyzing how decision-makers should rationally make decisions to gain the greatest possible advantage from their given situations. A few key terms that are commonly used in GT are as follows (Bhuiyan, 2018; McNulty, 2018):

  • (Strategic) Game: The formal description of any circumstance involving a strategic interaction of two or more decision-makers with a result that depends on the decision-makers’ actions. A game is called “non-cooperative” if players pursue their own interests at the expense of others’ (as a result of conflicting interests).
  • Player: Any decision-maker who takes actions in pursuit of his interests (within the context of the game) and whose actions affect the result of the game.
  • Actions: The set of available moves that the players are allowed to do in the game, which – therefore – defines the rules of the game being played.
  • Strategy: A complete plan of actions a player takes under particular situations in the game.
  • Payoff: The payout/utility quantity, measuring the total satisfaction that a player receives from a particular outcome of the game.
  • Nash Equilibrium: The stable situation, in which no player can gain any incremental benefit from changing his actions (and hence, would have no incentive to deviate from his current strategy) given the strategies of the others remain unchanged.
  • Zero-Sum Game:  A game, where no wealth is created and the net change in total utility is equal to zero as the total gains of winners are equivalent to the total losses of the other players.
  • Assumption of Rationality:  The assumption that players always make choices based on their rational outlook and strive to choose the actions that give the outcomes they most prefer (based on their expectation on other players’ strategies).

In general, the tools of OR have been used to manage organized systems and processes to achieve the optimal value for the chosen objective given the constraints and resources of the system/process of interest. Accordingly, the primary focus of the OR practitioners is on the particular system/process where the problem of interest arises, and the primary goal is to convert this real-life problem into a well-defined analytical problem that can be modeled and solved (Çağlayan, 2018). The steps of this process can be summarized as follows: (i) identifying the key decisions to be made and the key outcome (i.e., objective) to be improved, (ii) describing how these decisions affect the system behavior and the objective (via a mathematical formulation and/or programing code), (iii) using or developing the correct modeling approach capturing the constraints and key features of the system, (iv) using or designing an effective solution algorithm to identify optimal solutions, and (v) proving some of the important underlying properties of the systems of interest.

How the situation (or system) of interest is described, what its trade-offs are, and how certain actions affect the outcomes (of the situation) are also critical for GT. Yet, the focus of GT is not only on the situation itself (and its response to a decision-maker’s actions) but also on what other decision-makers do and the results of their actions. This aspect of GT makes it a powerful tool for studying the situations, where the outcome cannot be predicted or assessed accurately unless the choices (of multiple decision makers) affecting the result are analyzed within the same framework (rather than in isolation).

As a final note, I would like to state my personal opinion on the role of OR and GT in decision-making. Please take it with a grain of salt as it might be “a little” biased given I am an OR person.  The tools of OR such as linear programming, queuing theory and Markov decision process, are quite powerful in studying the complex systems and processes that are characterized by uncertainty, sequential decision-making, and/or many other challenging features. Accordingly, traditional OR methods might be more apt to analyze the behavior of complex systems and make better decisions for the management of such systems. Yet, the OR techniques generally only take into account what the system of interest do with respect to a decision-maker’s actions rather than what other decision-makers do (and how their actions affect the situation or a decision-maker’s strategy). On the other hand, GT is extremely suitable to study such circumstances and would be a more appropriate choice for analysis. As a result, depending on whether it is a complex system requiring advanced mathematical techniques to capture its key features and yield practical solutions or it is a strategic situation of cooperation or conflict where multiple decision-makers are involved, OR or GT would be the right approach offering an insightful evaluation of the particular case of study.

References

 Horner, P. (2015, December). Meet the ‘member in chief’.  OR/MS Today, Vol. 42, No. 6, pp. 36-41.

 Tanenbaum M., Eilon S., Holstein W.K., Ackoff R.L. Operations Research. In Encyclopedia Britannica online. Retrieved from https://www.britannica.com/topic/operations-research.

 Bhuiyan, B. (2018). An Overview of Game Theory and Some Applications. Philosophy and Progress, 59(1-2), 111-128. https://doi.org/10.3329/pp.v59i1-2.36683

 McNulty D. The Basics Of Game Theory. In Investopedia. Retrieved from https://www.investopedia.com/articles/financial-theory/08/game-theory-basics.asp#ixzz5XvqiB0F7

 Çağlayan Ç. (2018, November). The Use of Quantitative Methods with Two Different Perspectives: Data-Centric versus Problem-Centric. INFORMS OR/MS Tomorrow. Retrieved from https://www.informs.org/Publications/OR-MS-Tomorrow/The-Use-of-Quantitative-Methods-with-Two-Different-Perspectives-Data-Centric-versus-Problem-Centric