One of the most publicized parts of economics is the idea of game theory, popularized by Steve Nash and the film A Beautiful Mind. However, although some people understand the basics of this process, there are few that really comprehend how integral it is to business strategy. I am going to take you through a quick understanding of the different types of games in game theory and then provide reasons for how surpluses are distributed as a result of it. I could take for ages on this subject, and I definitely will, but consider this the first in a series of posts that will create the foundation for understanding.
To do this I will cite some authors of game theory; bare with me if you feel a little lost in the beginning as it will all come together in the end. In the simplest form, game theory is the idea that rational individuals will choose the outcomes that they believe will give them the biggest payoff given that their opponent(s) choose based on the same criteria. Hopefully you see the value in my research here and can understand why it took me a couple extra days to get this information up. I’ll be building on it in the future.
It is very true that game theory has its limitations, which will be further explored later, but the realities of its concepts are very real; individuals attach utilities and expected outcomes to future events and often make decisions based on these utilities, regardless of realization (Schniederjans, et al., 2010). Understandably, game theory does suggest economic rationality and there are some limits to the truth of that in the human experience, but in the context of high-level decision makers, or in the case of this paper, General Managers with high-paying, high-scrutinized job titles, decisions are rarely made lightly and without considering many of the possible alternatives. Regardless, there are some limits to perfect information.
But before stepping too far ahead, game theory itself must be examined for the success of these arguments. Simply put, game theory does not necessarily create a set of winners or losers. It is a tool that helps individual groups comprehend how choices can be interdependent (Papayoanou 2010: 5). As Papayoanou explains, “to determine this we need to first understand whether players’ choices can impact the values other players receive from different strategy alternatives; if so, the players’ choices are interdependent and contingent on the choices of others. This is the first condition. If that is true, we then need to ask if the actions we might take could affect the actions that others take, or vice versa. If so, influence issues exist (Papayoanou 2010: 7).”
The original major study of game theory stemmed from the works of von Neumann and Morgenstern’s 1944 volume titled Theory of Games and Economic Behavior (Breslau, 2003). Since then it has developed further, most often shown in the traditional form of a payoff matrix (Breslau, 2003). The game can take up to three forms: competitive games, coordination games, or collaboration games. Coordination games have the potential for a win-win opportunity while deviating from an agreement will result in a lose-lose situation. This is most often characterized by the Battle-Of-The-Sexes game. The payoff matrix is shown below to help illustrate this concept as well as to understand the payoff matrix that characterizes game theory:
To understand this diagram, consider a couple consisting of a man and a woman that are deciding which event to participate in on their Saturday night. The man prefers baseball while the woman prefers ballet; however, they also gain enjoyment from doing things together. Consider a case in which the man and the woman agree to attend the baseball game. The utilities are shown in the top left box (3,2). The man’s utility gained from attending the baseball game with the woman is shown as the first integer, or three in this case, while the woman’s utility gained from attending the baseball game with the man is shown as the second integer, or two in this case. Alternatively, if they both decided to attend the ballet together, the choice box would be the bottom right, creating the same integers though at reversed numbers. However, now consider that the man and woman decide to each pick the activity they would most prefer, baseball and ballet respectively. If they were to go individually the box chosen would be in the top right, creating utilities of one and one respectively. The bottom left box, which would be the result of illogical decision making, shows no utilities gained (Preston, 2012).
What does this game prove? It shows that the man and the woman gain utility from enjoying each other’s company, but also from doing the activity that each individually enjoys more. In this case there is a win-win scenario by agreeing to both do the same task so that they can be together. Perhaps a type of verbal contract can be communicated in which they agree to attend the baseball game this week and the ballet the following.
Conversely, Collaboration games have the possibility for a win-win but also an incentive to deviate from the original agreement in order to gain an advantage. Consider these games as the reason in which there are binding contracts in business. Perhaps the most notable game in this genre and throughout all of game theory is the Prisoner’s Dilemma. An image is represented below:
(Prisoner’s Dilemma, 2012)
For the sake of brevity, the background of this game suggests that there are two criminals locked in separate rooms without the means of communication. The detective presents each of them with the opportunity to point the finger at the other member in an attempt to get a reduced sentence. However, if they both accuse the other, they will both receive longer sentences than if they had both stayed quiet (Prisoner’s Dilemma, 2012).. The goal of this game is to prove that in almost all cases, both prisoners will choose to accuse the other individual, resulting in an undesirable situation for them both as the gains from staying quiet aren’t enough to compensate for the possibility of the other individual trying to gain an advantage (Breslau, 2003).
Lastly, competitive games are ones in which there is little incentive to work together or in which it is impossible. This is best characterized through the teenager-based game of Chicken, in which two individuals drive their cars at each other and the first person to swerve is considered a “chicken” and noted for their cowardice. In this situation there is clearly a lose-lose scenario, as crashing could not only injure or kill the individuals, but at the very least cause damages to their vehicles. It is impossible to achieve a win-win scenario, as necessarily one of the players must lose (unless both were to swerve at the same time, though for the sake of argument that possibility will be ignored, and it would more likely be considered a lose-lose scenario to the observers) (Papayoanou, 2010).
In reality, very few games fall completely into one category and the examples used above are extreme ones used to create easily identifiable visuals. Regardless, understanding their concepts is a necessity for understanding the rest of my arguments. Ultimately, as seen above, there are essentially five pieces that determine game theory: the key players, the choices available, the sequence in which choices are made, the key uncertainties, and the payoff available to each player in each outcome (Papayoanou, 2010).
Although there is much more information that needs to be conveyed (such as economic rationality, private information, bluffing, mixed strategies, and types of tactics), they will be explored in future posts for the sake of brevity and convenience.
In terms of the task at hand, it does not seem to have been explored in substantial depth, which is perhaps surprising given the wealth of data available. Baseball is convenient for a number of reasons in relation to game theory. Firstly, there is over one-hundred years of available statistics and data calculated that can testify to results. Secondly, baseball is a game that is easily understandable and comprehensible by the American audience. As Frederick Mosteller mentions in his work involving statistical valuation of pennant races, “if many reviewers are both knowledgeable about the materials and interested in the findings, they will drive the author crazy with the volume, perceptiveness, and relevance of their suggestions (Mosteller, 1997).” This relevancy makes it much easier to relate and understand the concepts as they are discussed. Finally, baseball is highly media-oriented, which creates the possibility for the utilization of tactics and posturing as well as understanding why not only the actual situations developed, but why alternatives perhaps didn’t.
Today, I only want to look at the idea of surpluses. If you recall, a player can gain a surplus if he gains a contract higher than the minimum he would have been willing to play for. Conversely, a team can gain a surplus if they sign a player to a contract lower than the maximum they would have been willing to pay him. This defines the idea of value.
Given the previous discussion, it is worth exploring why exactly each player does not receive the contract which puts his benefit identical (or at least close) to his cost. Perhaps the most obvious reason is that not all decision makers understand the argument that is being made here and instead choose to value players based on their relativity to other players with similar skill sets that are already signed. Secondly, some of the perfect measuring systems suggested simply do not exist, though part of the beauty of baseball is that there is quite a bit of data to draw on and the future can be at least partially predicted with relative accuracy. Thirdly, and the most important reason, however, is that general managers only want to pay the amount that produces the player so that costs can be reduced and thus profits increased. In short, teams wish to capture the producer surplus.
Although free agency is a competitive game with clear winners and losers, there are some variances in these truths. If it is to be assumed that each team has a limited budget with which to work, teams that don’t actually receive a free agent can “win” by convincing a competitor to pay more for a free agent than was necessary. By doing so, this detracts from the available resources for which them to purchase other free agents. In this way, even by “losing” in a free agent bidding war, a losing team can still somewhat win in the long run. This definitely happens, but there are some benefits to teams working in a collaboration game rather than a pure competitive game. To illustrate this, consider two gas stations located across the street from one another that only sell gas, a commodity with no differentiation abilities and similar operating costs as the business model is almost always identical. It could be possible that the two individuals that operate each gas station simply stand outside and constantly undercut their competitor by a penny in order to draw all the business. Following in this manner, the two would continue to constantly undercut until they reached a point of cutting costs further resulting in negative profits. Ultimately, the consumers would benefit in the lowest possible gasoline prices, but both of the owners would no longer be accruing a profit.
Alternatively, the two business owners could post a reasonable price and simply match one another. This is a form of signaling. By operating in this manner, the two gas station owners are able capture more of the surplus and garner a higher profit. Now although collusion is illegal in the American economy, the requirement for being convicted of such are, at the least, difficult to identify. Since free agency is a repeated game, although there is an incentive to force opposing teams to spend more than necessary, repercussions are likely in this scenario. In this way, the popular “tit for tat” game theory strategy can be employed.
While this explains in part why prices for free agents aren’t completely extreme, since future game costs must always be considered and teams wish to spend as little as possible to capture the player’s talents, there are other parties involved: the player, the agent, and the player’s collective bargaining agreement. The agent, which accrues a percentage of the player’s salary, is clearly incentivized to seek the highest value deal for the player. The collective bargaining agreement is the creation of the unionized Major League Baseball players. As with almost all unions, they seek the best benefits for the groups they represent, which is often based around money. Resultantly, the union often puts pressure on the player to accept the highest offer available to help create benchmarks/precedent of salary for other players that sign later. Lastly, the player himself has specific incentives. An important note of a player is that he is, obviously, a human, and thus gains utility from things besides pure monetary numbers, such as city that he lives in, competitiveness of the team, manager he would be playing under, guaranteed playing time (to parlay into a future contract usually), etc (Fishman, 2003). However, when considering the millions of dollars in play, those reasons would have to create significant utility in order to compensate for more than nominal decreases in salary.
Regardless, the point is that there is a group that is competing to maximize their surplus in comparison to the team’s surplus. Because of this it is understandable that the entire surplus is not captured by either group.
An important last note needs to be made and that is in the context of risk and uncertainty. Often analysts will talk about “money left on the table” by a player who signed with a team before the market developed or before receiving a team’s best offer. This is because people are often risk-averse and realize that there are comparable alternatives to their services, especially if the skills that the player brings are not extraordinary (Papayoanou, 2010). With the very real reality that a contract offer can disappear as team’s move onto other players and utilize their resources elsewhere, players may be tempted to minimize their risk by accepting a contract before they’ve maximized their personal surplus. Similarly, teams may engage in similar behavior, especially in negotiations with imperfect information.
Consider two teams vying for the same free agent left fielder where the next best alternative is significantly less desirable. Avoiding the legality of collusion, the only way that each team can know the amount the alternative team is offering is through information obtained by the agent and information publicly stated or leaked through the media. In this context, consider the power the agent has at commanding the surplus by acting shrewdly: he can suggest to each team that the other team’s offer is larger than theirs and that the only way to secure the free agent is to up the offered contract price. This process could theoretically continue until the surplus that would have been gained by each team is completely eliminated and a larger offer cannot be done.
In reality though, team officials understand the motives of the agent. As such, each team must determine the validity of the statement and how to act accordingly. If, in the situation, the team was to know that the statement that they were outbid was completely false, they would not raise their contract offer. If, in the situation, the team was to know that they were outbid by one million dollars (and they could increase it by still capturing profit), they would likely increase their bid by a million dollars and one penny. However, certainty is ever rarely true. As such, teams must decide how much to minimize their risk in relation to their reward; that is, at what point does increased guarantees of receiving the player reach a point of acceptable risk. As can be imagined, many of the previous questions come into play here: is there a relatively near substitute, will the competitor surpass the team if he is to be acquired there, etc.
Quantifying risk is extremely difficult and understanding the exact threshold which individuals are comfortable with understandably varies, though it is almost always dependent upon perceived payoffs. For now the important understanding is that there is an incentive to minimize risk from both groups and both are willing to pay premiums to acquire it. Note though, that since free agency is a repeated game, there are some incentives to not abuse the capabilities of psychological warfare as a “tit for tat” strategy may be employed.
Hopefully you followed my arguments here – I know I rehashed some previous sentiments but in a different light. I’ll further expand on game theory in the future, but in the end you should have realized from this that 1) Teams often signal to each other to avoid losing profits, 2) Game Theory is an important tool for analyzing potential payoffs and competitor’s moves, 3) That free agency is a repeated game and there are consequences to “annoying” your opponent, and 4) Money left on the table often happens because of an avoidance of risk.
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