Contribution Game Research Articles

Existence and verification of Nash equilibria in non-cooperative contribution games with resource contention

In resource contribution games, a class of non-cooperative games, the players want to obtain a bundle of resources and are endowed with bags of bundles of resources that they can make available into a common for all to enjoy. Available resources can then be used towards their private goals. A player is potentially satisfied with a profile of contributed resources when his bundle could be extracted from the contributed resources. Resource contention occurs when the players who are potentially satisfied, cannot actually all obtain their bundle. The player’s preferences are always single-minded (they consider a profile good or they do not) and parsimonious (between two profiles that are equally good, they prefer the profile where they contribute less). What makes a profile of contributed resources good for a player depends on their attitude towards resource contention. We study the problem of deciding whether an outcome is a pure Nash equilibrium for three kinds of players’ attitudes towards resource contention: public contention-aversity, private contention-aversity, and contention-tolerance. In particular, we demonstrate that in the general case when the players are contention-averse, then the problem is harder than when they are contention-tolerant. We then identify a natural class of games where, in presence of contention-averse preferences, it becomes tractable, and where there is always a Nash equilibrium.

Endogenous timing and income inequality in the voluntary provision of public goods: Theory and experiment

AbstractThis study theoretically and experimentally investigates the effects of income inequality on donors' decisions regarding timing choices and contributions to public goods when contribution timing is endogenously chosen by contributors. To this end, we use the conventional voluntary provision models of Warr (1983) and Bergstrom, Blume and Varian (1986), with Cobb–Douglas preferences augmented with a two‐stage game of Hamilton and Slutsky (1990). The following results were obtained and experimentally confirmed. First, when the distribution of income is extremely unequal, donors are indifferent between the simultaneous and sequential moves in the contribution game. Second, as income inequality is decreased, the simultaneous‐move contribution game is likely to emerge because every donor prefers to act as a leader. Nevertheless, a higher‐income donor may also prefer to act as a follower without specific social preferences and uncertainty regarding the quality of public goods. Third, most theoretical predictions regarding timing decisions are supported in our laboratory experiment, provided that the participants had enough time to learn the consequences of their timing choices.

Optimal Relative Performance Criteria in Mean-Field Contribution Games

We consider mean-field contribution games, where players in a team choose some effort levels at each time period and the aggregate reward for the team depends on the aggregate cumulative performance of all the players. Each player aims to maximize the expected reward of her own share subject to her cost of effort. To reduce the free-rider issue, we propose some relative performance criteria (RPC), based on which the reward is redistributed to each player. We are interested in those RPCs that implement the optimal solution for the corresponding centralized problem, and we call such RPC an optimal one. That is, the expected payoff of each player under the equilibrium associated with an optimal RPC is as large as the value induced by the corresponding problem where players completely cooperate. We first analyze a one-period model with homogeneous players and obtain natural RPCs of different forms. Then, we generalize these results to a multiperiod model in discrete time. Next, we investigate a two-layer mean-field game. The top layer is an interteam game (team-wise competition), in which the reward of a team is impacted by the relative achievement of the team with respect to other teams; the bottom layer is an intrateam contribution game where an RPC is implemented for reward redistribution among team members. We establish the existence of equilibria for the two-layer game and characterize the intrateam optimal RPC. Finally, we extend the (one-layer) results of optimal RPCs to the continuous-time setup as well as to the case with heterogenous players.

Promoting socially desirable behaviors through persuasion and commitment: Experimental evidence

Through a series of experiments, this paper tests the relative efficiency of persuasion and commitment schemes to increase and sustain contribution levels in a Voluntary Contribution Game. The design allows us to compare a baseline consisting of a repeated public good game to four treatments of the same game in which we successively introduce a persuasion message, commitment devices, and communication between subjects. Our results suggest that these non-monetary procedures significantly increase cooperation and reduce the decay of contributions across periods.

The sophistication of conditional cooperators: Evidence from public goods games

We extend the study of behavioural types in voluntary contribution games, adapting the elicitation method of Fischbacher et al. (2001) to a broader range of economic and strategic incentives. Our results in the standard VCM game align with previous findings in many respects; in particular, we identify one-quarter of participants as a distinctive group of “strong” conditional cooperators. We provide an explanation for the behaviour of this group by tracking their contribution strategies as the financial incentives of the game vary. We find that conditional cooperators follow a sophisticated rule, matching contributions only when doing so leads to an overall welfare improvement. This favours an account of conditional cooperation based on social norm compliance, rather than confusion, inequity aversion, or warm-glow giving.

Contribution games with asymmetric agents

We generalise Admati and Perry (1991)’s two-player, alternating contributions model, allowing participants to be asymmetric from two dimensions: 1. one of the players is the deadline player and 2. players receive different rewards on completing the project. In equilibrium, the project either ends in the first few stages or at the deadline. A slight change in the environment can influence the ending time dramatically. Based on that, we discuss the appropriate rewarding distribution.

Leveraging the Honor Code: Public Goods Contributions under Oath

Public good games are at the core of many environmental challenges. In such social dilemmas, a large share of people endorse the norm of reciprocity. A growing literature complements this finding with the observation that many players exhibit a self-serving bias in reciprocation: “weak reciprocators” increase their contributions as a function of the effort level of the other players, but less than proportionally. In this paper, we build upon a growing literature on truth-telling to argue that weak reciprocity might be best conceived not as a preference, but rather as a symptom of an internal trade-off at the player level between (i) the truthful revelation of their private reciprocal preference, and (ii) the economic incentives they face (which foster free-riding). In truth-telling experiments, many players misrepresent private information when this is to their material benefit, but to a significantly lesser extent than what would be expected based on the profit-maximizing strategy. We apply this behavioral insight to strategic situations, and test whether the preference revelation properties of the classic voluntary contribution game can be improved by offering players the possibility to sign a classic truth-telling oath. Our results suggest that the honesty oath helps increase cooperation (by 33% in our experiment). Subjects under oath contribute in a way which is more consistent with (i) the contribution they expect from the other players and (ii) their normative views about the right contribution level. As a result, the distribution of social types elicited under oath differs from the one observed in the baseline: some free-riders, and many weak reciprocators, now behave as pure reciprocators.

On a Mechanism that Improves Efficiency and Reduces Inequality in Voluntary Contribution Games

On a Mechanism that Improves Efficiency and Reduces Inequality in Voluntary Contribution Games

Interacting Corporate Political Activities with Evidence from the Tobacco Industry

AbstractResearch on firm-level corporate political activity often treats firm-government interactions as independent of the market competition between firms. Yet, firms that compete in the market will consider rivals when making strategic nonmarket decisions. Ignoring market rivalry when studying nonmarket strategy introduces fundamental endogeneity problems and potentially overlooks a central mechanism explaining firms’ political choices. Our study demonstrates this by investigating the strategic nonmarket interactions of large US tobacco manufacturers, a case study that is independently interesting. From 1992 to 2008, the US tobacco industry experienced dramatic upheaval in its business environment as regulatory authority shifted from the state to federal level, under the Food and Drug Administration. Using firm-candidate–cycle data, a complete information campaign contributions game, played in the nonmarket environment, is estimated for two of the United States’ largest tobacco manufacturers. Results demonstrate that, rather than acting in isolation, US tobacco firms strategically coordinated their firm-level political campaign contributions.

Teamwise Mean Field Competitions

This paper studies competitions with rank-based reward among a large number of teams. Within each sizable team, we consider a mean-field contribution game in which each team member contributes to the jump intensity of a common Poisson project process; across all teams, a mean field competition game is formulated on the rank of the completion time, namely the jump time of Poisson project process, and the reward to each team is paid based on its ranking. On the layer of teamwise competition game, three optimization problems are introduced when the team size is determined by: (i) the team manager; (ii) the central planner; (iii) the team members’ voting as partnership. We propose a relative performance criteria for each team member to share the team’s reward and formulate some special cases of mean field games of mean field games, which are new to the literature. In all problems with homogeneous parameters, the equilibrium control of each worker and the equilibrium or optimal team size can be computed in an explicit manner, allowing us to analytically examine the impacts of some model parameters and discuss their economic implications. Two numerical examples are also presented to illustrate the parameter dependence and comparison between different team size decision making.

Game Theory for Systems Engineering: A Survey

Game theory is a useful modelling approach to analyse complex systems with multiple stakeholders, describe their decision-making process, and the impact these decisions have on the overall system performance. In this paper, we review the use of game theory models in the systems engineering domain. Our approach was to conduct an extensive literature review in systems engineering related journals on game theory and systems engineering content. We have identified major application areas of game theory within systems engineering, such as electricity markets, security systems, and supply chain; which we discuss in detail. This paper aggregates notable research to date to provide an overview of the models that have been used to analyse different systems engineering problems. The paper also provides an extensive description of different game properties. This work aims to highlight the potential contribution game theory brings to solving systems engineering problems and its potential for the future.

Ethnic Heterogeneity and Public Goods Provision

The level of public goods provided in a society is important not only because it contributes to social inclusion and strengthens a shared sense of citizenship, but also because it is a fundamental pre-condition for long term growth and development. Studying the determinants of public goods provision levels, hence, becomes an important exercise. The negative association between ethnic heterogeneity and public goods provision is one such robust empirical finding in political science and economics. Despite the abundance of scholarly work on the topic, the causal mechanisms offered in the literature do not pay attention to the political process involved. The rational choice approaches simply model the relationship as a voluntary contribution game. This paper addresses this gap by offering a theoretical mechanism based on a legislative bargaining framework. We also provide a discussion on a potential extension of the framework where ethnic groups are endogenous.

Household tax evasion

AbstractHousehold members share public goods and make intra‐household transfers. We show how these features of the household interact with the tax evasion decision, and identify the dimensions in which household evasion differs from individual evasion. In the model we present two members of a household choose how much to contribute to a household public good and how much self‐employment income to evade. We are interested in how different evasion possibilities interact with the contribution decisions to the household public good and the role of income transfers within the household. We show the household evasion decision differs from the individual decision because it affects the outcome of the household contribution game. When household members are taxed as individuals neutrality applies when choices are not constrained. If the evasion level of one household member is constrained then an income transfer can generate a Pareto improvement. When the household members are jointly taxed there is a couple constraint on strategies and corner solutions can emerge.

Contribute once! Full efficiency in a dynamic contribution game

Dynamic public good contribution games in the literature allow players to contribute in multiple periods. These games typically have inefficient and, sometimes, (approximately) efficient subgame perfect equilibria. Inefficiency can take the form of either delayed provision or nonprovision of the public good. In contrast, this paper studies a game that differs primarily in that each player can contribute only once. Each player thus chooses the period at which they contribute, and the size of the contribution. The main result is that if the number of periods is finite but larger than the number of players, then every subgame perfect equilibrium in which each player's contribution amount is strictly less than that player's valuation for the good is efficient: the public good is provided without delay.

Group size and collective action in a binary contribution game

We consider how group size affects the private provision of a public good with non-refundable binary contributions. A fixed amount of the good is provided if and only if the number of contributors reaches an exogenous threshold. The threshold, the group size, and the identical, non-refundable cost of contributing to the public good are common knowledge. Our focus is on the case in which the threshold is larger than one, so that teamwork is required to produce the public good. We show that both expected payoffs and the probability that the public good is obtained in the best symmetric equilibrium are decreasing in group size. We also characterize the limit outcome when group size converges to infinity and provide precise conditions under which the expected number of contributors is decreasing or increasing in group size for sufficiently large groups.

Should the Talk be Cheap in Contribution Games?

AbstractThis paper studies the equilibria of contribution games with commitment and with cheap talk under incomplete information. When agents contribute to a club good, we find that with commitment, high types contribute early to induce low types to contribute in later rounds. With cheap talk, low types signal to contribute early but may drop out later if they find the total contributions are low. When there are sufficiently many rounds, we construct a cheap talk equilibrium that implements the ex-post efficient and ex-post individually rational allocation. In contrast, every equilibrium of the commitment game is inefficient. When the good is a public good, the cheap-talk game admits no informative equilibria. In this case, the equilibria of the commitment game may be more efficient.

Words and deeds – Experimental evidence on leading-by-example

The paper studies how leadership recommendations and leading-by-example shape group behavior. The experimental results from an intergroup contest show that the leaders are the key drivers of contest expenditure. They increase their expenditure substantially once they make recommendations to the followers. The leaders' expenditure recommendations have a highly significant impact on the investments of followers. The additional impact of leading by example confirms the relevance of the alignment of words and deeds. A second experiment replicates the treatments in a non-competitive voluntary contribution game. In this setting, the opportunity for making recommendations has an even stronger impact on the leader's expenditure. For a given level of leader expenditure, the behavior of followers remains remarkably consistent across the two experiments but the additional impact of leading by example is not significant anymore.

Optimal Relative Performance Criteria in Mean Field Contribution Games

We consider mean-field contribution games, where players in a team chooses some effort level at each time period, and the aggregate reward for the team depends on the aggregate cumulative performance of all the players. Each player aims to maximize the expected reward of her own share subject to her cost of effort. To reduce free-rider issue, we propose some relative performance criteria (RPC), based on which the reward is redistributed to each player. We are interested in those RPCs which implement the optimal solution for the corresponding centralized problem, and we call such RPC an optimal one. That is, the expected payoff of each player under the equilibrium associated with an optimal RPC is as large as the value induced by the corresponding problem where players completely cooperate. We first analyze a one-period model with homogeneous players, and obtain natural RPCs of different forms. Then we generalize these results to a multi-period model in discrete time. Next, we investigate a two-layer mean-field game: The top-layer is an inter-team game (team-wise competition) in which the reward of a team is impacted by the relative achievement of the team with respect to other teams; the bottom layer is an intra-team contribution game where an RPC is implemented for reward redistribution among team members. We establish the existence of equilibria for the two-layer game and characterize the intra-team optimal RPC. Finally, we extend the (one-layer) results of optimal RPCs to the continuous-time setup as well as to the case with heterogenous players.

Teamwise Mean Field Competitions

This paper studies competitions with rank-based reward among a large number of teams. Within each sizable team, we consider a mean-field contribution game in which each team member contributes to the jump intensity of a common Poisson project process; across all teams, a mean field competition game is formulated on the rank of the completion time, namely the jump time of Poisson project process, and the reward to each team is paid based on its ranking. On the layer of teamwise competition game, three optimization problems are introduced when the team size is determined by: (i) the team manager; (ii) the central planner; (iii) the team members' voting as partnership. We propose a relative performance criteria for each team member to share the team's reward and formulate some special cases of mean field games of mean field games, which are new to the literature. In all problems with homogeneous parameters, the equilibrium control of each worker and the equilibrium or optimal team size can be computed in an explicit manner, allowing us to analytically examine the impacts of some model parameters and discuss their economic implications. Two numerical examples are also presented to illustrate the parameter dependence and comparison between different team size decision making.

Research on collaborative construction of multiple subjects inside and outside the engineering project team: Based on the perspective of principal-agent theory

During the construction of the project team, many problems are faced. Based on the game theory perspective of principal-agent, this paper constructs and analyses the game model inside and outside the engineering project team. The results show that: (1) in the internal knowledge contribution game of engineering project team, there is a game model of “Prisoner’s Dilemma” among members. The final choice is often not to participate in the knowledge contribution, and this will damage its actual interests; (2) under the principal-agent game model of the contractor and the engineering project team, the engineering project team needs to continuously increase knowledge and improve technology to achieve the increase of marginal revenue; (3) in the three-party principal-agent game model of the owner, contractor and supervisor, the rent-seeking relationship between the supervisor and the contractor will affect the overall project efficiency, so it should be particularly vigilant. Finally, based on the above results, the countermeasures and suggestions for the collaborative construction management of multi-agents inside and outside the engineering project team are proposed.