The gift-exchange game, also commonly known as the gift exchange dilemma, is a common economic game introduced by George Akerlof and Janet Yellen to model reciprocacy in labor relations. The gift-exchange game simulates a labor-management relationship execution problem in the principal-agent problem in labor economics. The simplest form of the game involves two players – an employee and an employer. The employer first decides whether they should award a higher salary to the employee. The employee then decides whether to reciprocate with a higher level of effort (work harder) due to the salary increase or not. Like trust games, gift-exchange games are used to study reciprocity for human subject research in social psychology and economics. If the employer pays extra salary and the employee puts in extra effort, then both players are better off than otherwise. The relationship between an investor and an investee has been investigated as the same type of a game.
The gift exchange game serves as a valuable lens through which to understand economic theory as it demonstrates that self-interest maximization is not the sole determinant of economic decision-making. Rather, reciprocity is a fundamental factor that shapes individuals' behaviour in economic contexts. By simulating labor relations between an employer and employee, the game explicates that when employer offer a higher salary, employees are more inclined to reciprocate with great effort, leading to mutually beneficial outcomes. Gift exchange games have been used to study economic and social phenomena such as labor contracts, market transactions, strike and the decline of unionization. The gift-exchange theory also incorporates a social component, where homogenous agents who are employed with an equivalent wage level will exert greater effort. This then continues to result in a higher market efficiency and higher rent than those agents receiving different wages. The first examination of this component is referred to as the fair uniform-wage hypothesis, where experiments establish the significant efficiency premium of uniform wages. However, this is not a consequential result of a stronger level or reciprocity by the agents, although the reinforcement of endorsing these options on the side of principals with uniform wages is why implementing boundaries to freedom can lead to efficiency-enhancing results.
Equilibrium analysis
In the game theory, the equilibrium analysis can be implemented to determine and examine strategic decisions between the players in a game. Nash equilibrium is the situation of a game where no player has an incentive to change the strategy given the strategic decision based on the other player. It is implemented to evaluate these situations and the decisions by the players that are made affecting each players out come. The extra effort in gift-exchange games is modelled to be a negative payoff if not compensated by salary. The IKEA effect of own extra work is not considered in the payoff structure of this game. Therefore, this model rather fits labor conditions, which are less meaningful for the employees.
Like in trust games, game-theoretic solution for rational players predicts that employees’ effort will be minimum for one-shot and finitely repeated interactions. The difference constitutes by the sequentiality of gift-exchange game. In the gift exchange game, the employer pays a high or low salary first and then the employee makes the decision. So employers have no incentive to pay high salaries if workers know what they are choosing. If the employer pays a higher salary, it is irrational for the employee to put extra effort, since effort will reduce his or her payoff. It is also irrational for the employee to put extra effort while receiving a lower salary. Therefore, the minimum salary and the minimum effort is the equilibrium of this game.
As this game is considered a perfect information game where all players are aware of previous actions, backwards induction can also be used to determine the equilibrium of this game. As both players are rational, they will both work to maximise their utility. Looking at game tree shown on the right, the last decision is determined by the employee. The utilities for the employer and employee are outlined in red and blue respectively. In both a high and low salary option, the employee will benefit more from choosing the low effort option. In a high salary path, the high effort choice yields a utility of 2 for the employee whereas in the low effort path the utility is 3. In the low salary high effort path, the employees utility will be 0 compared to the low effort choice which results in a utility of 1. Thus the employee will choose low effort regardless of the salary choice made by the employer. Moving a decision back, it is now the employers choice between high or low salary. Knowing the employee will choose low effort, the employer will also choose the option that maximises their utility. In the high salary low effort option, their utility eventuates to 0 whereas in the low salary low effort option, their utility is 1. Knowing the employee will choose the low effort option as it maximises their utility, the employer will choose low salary. This will lead to the equilibrium of low salary and low effort.
Contrast with Prisoner's dilemma
The payoff matrix of the gift-exchange game has the same structure as the payoff matrix of prisoner's dilemma when strategies are involved in the decision-making between the players. However, there are key differences between the two games. The difference constitutes by the sequentiality of gift-exchange game, with the gift exchange games being based on social norms of reciprocity, where participants are incentivized to act in ways that other players deem fair. The goal of the game is to maximize the amount of money each player receives, and to follow the expectations of the group. Although, in contrast to the prisoner's dilemma two participants are faced with either cooperation or betrayal, without knowing what the other players will decide and the payoff of each possible outcome is determined by the choices of both players. The prisoner's dilemma aims to show how rational decisions can lead to sub-optimal outcomes for both parties, even when cooperation is in the best interest of both parties.S Kuhn. (1997). Prisoner’s dilemma (Stanford encyclopedia of philosophy). Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/prisoner-dilemma/ The goal of both games is to maximize the amount of money each player receives, but in the prisoner's dilemma, rational decisions can lead to sub-optimal outcomes for both parties, even when cooperation is in the best interest of both players. In the gift-exchange game, the choices of all players are interdependent, and the social norms of reciprocity incentivize participants to act in ways that benefit the group as a whole. In our follow-up experiments with the gift exchange game, we found that only a few people in the real world would choose the minimum wage and minimum effort to reach the Nash equilibrium.
Experimental Methods and Results
A positive relationship between salary and effort has been observed in a large number of gift-exchange experiments performed in a laboratory setting. This behaviour obviously deviates from the equilibrium.
A study on 84 undergraduate students at the University of Amsterdam was conducted to observe the difference in findings that were predicted to occur when the gift-exchange game performed between one employer one employee was compared to a game performed between one employer and four employees. The results indicated the number of employees did not have a significant impact on the level of effort that was chosen, with both mean effort levels increasing with wage at similar rates.
Another experiment with students from Tilburg University showed that only 33% of games ended up in the Nash equilibrium with minimal salary and minimal effort. Data from another experiment on 123 students from University of Nottingham showed a rate of 69% for high salary being paid by employer in advance.
Fehr, Kirchsteiger and Riedl (1993, QJE) designed a market in which "employers" and "employees" do not meet. All wages and effort and "employees" are put in different rooms for many experiments, and are told that the counterparties of each transaction are different, and both sides keep "anonymous" transactions from beginning to end. In this way, the influence of expectations of both sides on the "long-term future" is excluded, and the choice of the level of effort of "employees" is completely self-conscious. According to the traditional economic view, employees will be willing to accept any wage greater than 0, and provide the minimum level of effort after receiving the salary. However, the experimental results show that employers always offer wages much higher than the minimum level, while employees almost always provide efforts much higher than the minimum level. This proves that even if there are no other supervision and punishment mechanisms, the wage level in the labor market is often higher than the market-clearing price for some "fair" and "goodwill" motives in exchange for the labor provider's initiative and loyalty. It's also an example of how social norms and reciprocity can affect human behavior even in the absence of regulation.
The experiment of charness (2000, JEBO) wanted to explore what would happen if the benefit of high wages was not given by the employer but a random result or a third party. The results of this experiment are as follows: (1) if wages are generated randomly, employees usually give extra efforts to show "fairness" or compensation, considering that they are after all the employer's money. (2) If, at almost the same income level, employees are told that the wage level is determined by the experimenter, they will think that they don't have to pay a lot of responsibility for the "loss" to the employer, so they will relatively reduce their efforts.
Gneezy and List (2006, Econometrica) were two of the first economists to investigate whether similar results found in the previous laboratory experiments could be replicated in a field setting. They did so by conducting two separate experiments, each involving a number of volunteer participants who were required to perform a specific task for six hours in total. Each participant would receive an hourly wage that had been previously advertised to them. The participants in each experiment were divided into two groups, one of which were informed that the actual wage they would be receiving was higher than the wage advertised to them. Each of the two experiments yielded similar results. For both experiments, the group receiving the increased wage only performed the task more efficiently in the initial stage of the task. Towards the end of the six hours, the groups yielded similar outputs and were performing at the same productivity level. While these results are inconsistent with previous laboratory finds, they endorse one feature of "reciprocal behaviour", that is, as time goes on, preferential treatment will be taken for granted, thus reducing the willingness of employees to supply labour.