Game theory has always played a role in conflict and cooperation studies. It is a concept applied where agents’ actions are interdependent. The agents may be individuals, groups or a combination of both. Through its concepts, one can be able to understand strategic scenarios while formulating, structuring and analyzing them.
Game theory began as a mathematical approach in the 1940s. It was not until 1957 that the concept was further developed and applied in social science. From this development, came a new definition of game theory. Game theory was now known as a branch of mathematical logic “that underlies real conflicts among (not always rational) humans” (Geisler, 2014).
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Game theory is an application of mathematical models in decision-making. It is used to predict the outcome of decisions made by two people during an interaction. People participating in the games are known as ‘players’. The decisions they make are known as ‘strategies’ and their outcomes are ‘pay-offs’ (Norton, 2016).
Studying the game is the objective of game theory (Turocy & Stengel, 2001). These games have two levels, cooperative or coalitional, and noncooperative. In cooperative games, pay-offs that can be obtained by each cooperating group are specified. In noncooperative games, choices are made by players out of their own interest.
Cooperative game theory can, therefore, be defined as the investigation of cooperative games to determine how proceeds should be divided by a coalition. On the other hand, noncooperative game theory analyzes strategic choices by providing a process which prespecifies who makes an offer and at what time (Turocy & Stengel, 2001).
Although the game levels are different, they share a common assumption. Rationality of the players is the common assumption in game theory (Turocy & Stengel, 2001). A rational player is always making choices that will maximize their pay-offs. This paper will focus on noncooperative game theory.
There are two forms of noncooperative games, the strategic and extensive (Turocy & Stengel, 2001). The strategic form is also known as the normal form and entails the listing of each player’s strategies and their outcomes. The extensive form is also known as a game tree and entails a complete description of the gameplay such as the order of actions taken by each player.
When discussing games under game theory, then the prisoner’s dilemma comes to mind. Two criminals are brought in to be interrogated. If they cooperate, then they get lesser charges and serve only two years. If one defects, he gets one year in prison while the other gets five years (Satell, 2009). If both choose to defect, each criminal gets three years in prison.
The prisoner’s dilemma is a strategic game between two players. This approach can be described as “a transposition between cooperation and betrayal between two interacting parties” (Geisler, 2014). While both players benefit from not talking, the dominant strategy is to talk (Satell, 2009). By talking they both get lesser sentences compared to if they both kept quiet.
Game theory plays a significant role in procurement. Initially, it was ignored by businesses until the 1994 telecom auctions in the United States (Norton 2016). However, it is now used in sales and marketing and even research and development. The game theory can also be applied in procurement.
As stated before, the game theory came into play in the 1994 telecom auction in the US. The auctions were for 3G licenses and were designed to be competitive. The licenses being offered were fewer in number than the number of telecom operators bidding. The bidders were put in a difficult situation akin to the prisoner’s dilemma.
If the telecom operators failed to bid, then they would be locked out of a lucrative business. The operators were therefore forced to make high bids. However, the successful operators incurred debts because of this decision. They were left unable to purchase equipment necessary for the 3G licenses.
Looking at a hypothetical conflict can help one understand the application of game theory in procurement. Suppose we have a negotiation on security camera installation for an African country, player 1 is the company to install the security cameras and player 2, is the African country.
The installation company can choose to offer two packages. The first package is to install security cameras with built-in video analysis software. The second package is to install security cameras without the video analysis software. The details of these packages are not included in the contract and costs will be incurred by the company whether the contract is signed or not.
| Player 2 (African country) | |||
| Player 1(Company) | Install | Do not install | |
| First Package | 2-2 | 0-1 | |
| Second Package | 3-0 | 1-1 | |
| Payoff overview of the negotiation on security camera installation | |||
The first package will cost the company more while the second package will cost less. The first package is valuable to the country than the second. In fact, the country would not choose the second package if they were aware it would not benefit them. The country has two choices, to install the cameras or not to install them at all.
The country will prefer to install the cameras if the installation company provides cameras that are valuable to them, and not to install if otherwise. However, whether the country approves the installation of the cameras or not, the company will always prefer to install the second package. This second package is the dominating strategy.
The African country, player 1, is aware the installation company, player 2 is rational. Therefore, the country will anticipate the installation of the second package. The country will choose not to install the cameras on this basis. This gives the country a payoff of 1 compared to 0 if it installed the cameras. The contract will therefore not be signed.
In this hypothetical conflict, the preferences of player 2 are dependent on the actions of player 1. The conclusion is the country has no dominating strategy, but the company does. If the company chooses to eliminate the first package option, then the country is more likely to install the cameras. Other strategies to alter the outcome of this conflict are discussed below.
The minimax theorem can be applied to help come to an agreement in this negotiation. The theorem states “you should pick the strategy where the maximum advantage of your opponent is minimized” (Satell, 2009). The country may choose to only allow installation and signing of the contract if the company promises to install the first package.
Another strategy that can be used in this scenario is Nash’s equilibrium. The equilibrium offers a strategy to each player which cannot be improved on unilaterally if the other player accepts the strategy (Turocy & Stengel, 2001). All players are rational and will accept the strategy as they believe the other player will do the same.
One strategy for Nash’s equilibrium is the combination of the second package with the choice of not installing the cameras. This strategy will force the company to only offer the first package to allow installation. The company will benefit from not losing out on the contract while the country will benefit from installing valuable security cameras.
The other strategy could be to offer the first package if the country agrees to install the camera. The company will prefer to install the first package if only the contract is signed. On the other hand, the country will prefer the first package because it is more valuable to them. This second strategy offers more pay-offs than the first (payoff of 2-2 compared to that of 1-1).
Another way to alter the outcome of this negotiation is through making promises and threats. For example, the country can promise to sign the contract if the company offers the first package. On the other hand, the company can choose to threaten the company that it will not install the first package until the country agrees to sign the contract.
The game theory consists of mathematical models that may have unrealistic assumptions. However, from these assumptions, we can gain principles that are useful in actual negotiations. According to Satell (2009), these principles are as follows:
Minimizing risk to guarantee your opponent does not get a maximum payout.
Making the first offer to have the negotiation to your advantage.
Do not accept a situation that puts you at a disadvantage.
Be trustworthy. It is better to incur cost than lose stature.
All negotiations should be open-ended to encourage continuity.
Whatever choice you make is what you will get in return.
Game theory is a great tool for procurement. It offers an opportunity for both players to determine the outcomes of their actions about the negotiations. Any game should always fulfill the assumption of rationality and self-interest. These assumptions build the basis for the game’s setting.
While its applications in procurement are beneficial, there is still a need to do more research in game theory. This research will increase understanding of the theory in procurement. It would also facilitate its expansion into other fields when more rule and guidelines are introduced.
References
Geisler M. (2014). The Impact of the Game Theory in Supply Chain Management. Retrieved 30 January 2018, from https://pdfs.semanticscholar.org/08e2/bc3ad66b98498d8816c9419483012dbad85e.pdf
Norton S. (2016, March 20). Game Theory in Procurement. LinkedIn. Retrieved 30 January 2018, from https://www.linkedin.com/pulse/game-theory-procurement-steven-norton
Satell G. (2009, November 29). A Guide to Game Theory and Negotiations. DigitalTonto. Retrieved 30 January 2018, from https://www.digitaltonto.com/2009/game-theory-guide-to-negotiations/
Turocy L. T., Stengel B. (2001). Game Theory. Retrieved 30 January 2018, from http://www.cdam.lse.ac.uk/Reports/Files/cdam-2001-09.pdf
