Provision Game Research Articles

Pareto optimal provisions as outcomes of voluntary public good supply

It is shown that a large set of public good supply levels that arise in a Pareto optimal allocation can also be attained as public good provisions in the Nash equilibrium of a non-cooperative provision game. With a not very far-fetched assumption on agents’ preferences this result even holds for all Pareto supply levels.

Modeling collaborative data service provision around an open source platform under uncertainty with stochastic provision games

This paper uses concepts taken from Cooperative Game Theory to model the incentives to join forces among a group of agents involved in collaborative provision of a mobile app under uncertainty around an open source platform. Demand uncertainty leads the agents to reach a noncooperative equilibrium by offering low quality apps. This can be avoided by introducing a coordination scheme through a common platform that eliminates the effects of lack of information. Coordination is achieved by providing a revenue sharing scheme enforcing the stability of the collaboration but also defined in a “fair” way, depending on the importance of the resources that each provider supplies to the app. To this aim, we introduce the concept of Stochastic Provision Games. This coordination leads both to higher app quality and improved profitability for the participants.

Power asymmetry in repeated play of provision and appropriation games

This paper studies the effect of power asymmetry on resolution of social dilemmas in repeated play of linear public good games. The experiment uses a 2 × 2 design that crosses power symmetry or asymmetry in payoff-equivalent provision and appropriation games with positive (provision) or negative (appropriation) externalities. Power asymmetry combines privileged access to information with extended opportunity sets that allow for taking a public good provided or not-appropriated by others. Our data suggest that power asymmetry has a detrimental effect on efficiency, with the effect being more pronounced in the asymmetric-power appropriation game. Individual allocations to the public good increase in others’ allocations, suggesting that individual allocations are not strategic substitutes. With power asymmetry, first movers earn less than the second mover in the appropriation game but not in the provision game.

The Stackelberg vs. Nash-Cournot Folk-theorem in international environmental agreements

A commonly reported result in the literature on international environmental agreements (IEAs) is that if coalition members act as Stackelberg leaders (Stackelberg scenario) this leads to larger stable coalitions than if signatories act simultaneously with non-signatories (Nash-Cournot scenario). This result has been taken for granted, a kind of Folk-theorem, even though it has been proven at best for specific payoff functions, and very often the conclusion is only based on simulations. We prove the Stackelberg vs. Nash-Cournot Folk-theorem based on a generic payoff function for a public good provision game.

Morally monotonic choice in public good games

Rational choice theory, including models of social preferences, is challenged by decades of robust data from public good games. Provision of public goods, funded by lump-sum taxation, does not crowd out private provision on a one-for-one basis. Provision games elicit more of a public good than payoff-equivalent appropriation games. This paper offers a morally monotonic choice theory that incorporates observable moral reference points and is consistent with the two empirical findings. The model has idiosyncratic features that motivate a new experimental design. Data from our new experiment and three previous experiments favor moral monotonicity over alternative models including rational choice theory, prominent belief-based models of kindness, and popular reference-dependent models with loss aversion.

Shadow of conflict: How past conflict influences group cooperation and the use of punishment

Intergroup conflict profoundly affects the welfare of groups and can deteriorate intergroup relations long after the conflict is over. Here, we experimentally investigate how the experience of an intergroup conflict influences the ability of groups to establish cooperation after conflict. We induced conflict by using a repeated attacker-defender game in which groups of four are divided into two ‘attackers’ that can invest resources to take away resources from the other two participants in the role of ‘defenders.’ After the conflict, groups engaged in a repeated public goods game with peer-punishment, in which group members could invest resources to benefit the group and punish other group members for their decisions. Previous conflict did not significantly reduce group cooperation compared to a control treatment in which groups did not experience the intergroup conflict. However, when having experienced an intergroup conflict, individuals punished free-riding during the repeated public goods game less harshly and did not react to punishment by previous attackers, ultimately reducing group welfare. This result reveals an important boundary condition for peer punishment institutions. Peer punishment is less able to efficiently promote cooperation amid a ‘shadow of conflict.’ In a third treatment, we tested whether such ‘maladaptive’ punishment patterns induced by previous conflict can be mitigated by hiding the group members’ conflict roles during the subsequent public goods provision game. We find more cooperation when individuals could not identify each other as (previous) attackers and defenders and maladaptive punishment patterns disappeared. Results suggest that intergroup conflict undermines past perpetrators’ legitimacy to enforce cooperation norms. More generally, results reveal that past conflict can reduce the effectiveness of institutions for managing the commons.

Measures against the abandonment of common property summer pastures: experimental evidence from joint appropriation–provision games

Measures against the abandonment of common property summer pastures: experimental evidence from joint appropriation–provision games

Permissioned Distributed Ledgers and the Governance of Money

We explore the economics and optimal design of “permissioned” distributed ledger technology (DLT) in a credit economy. Designated validators verify transactions and update the ledger at a cost that is derived from a supermajority voting rule, thus giving rise to a public good provision game. Without giving proper incentives to validators, however, their records cannot be trusted because they cannot commit to verifying trades and they can accept bribes to incorrectly validate histories. Both frictions challenge the integrity of the ledger on which credit transactions rely. In this context, we examine the conditions under which the process of permissioned validation supports decentralized exchange as an equilibrium, and analyze the optimal design of the trade and validation mechanisms. We solve for the optimal fees, number of validators, supermajority threshold and transaction size. A stronger consensus mechanism requires higher rents be paid to validators. Our results suggest that a centralized ledger is likely to be superior, unless weaknesses in the rule of law and contract enforcement necessitate a decentralized ledger.

Expectational stability in aggregative games

In aggregative games individuals’ payoffs depend on players’ own contributions (or strategies) and on the aggregate contribution of other players. The replacement function, which defines the optimal contribution of a player in an aggregate contribution, is a convenient tool to analyze aggregative games. In this paper, the replacement function is used to define an adjustment process of expectations with respect to the aggregate strategy of the game. The Nash equilibrium of the game is interpreted as the rational expectations equilibrium (REE) of the dynamical system defined by that adjustment process. The expectational stability of the REE is analyzed and its local stability is characterized in terms of the fundamentals and the REE itself. Stronger results of global stability can be obtained when the model is applied to specific aggregative games with explicit payoff functions. Examples of Cournot oligopoly and public goods provision games are presented to illustrate global stability.

Who will watch the watchers? On optimal monitoring networks

Consider a moral hazard scenario in which a monitor must detect deviations to provide proper incentives to attain an efficient outcome. What if the monitor himself were to deviate after being bribed by his monitored subject? In this paper, I model a multi-agent public-good provision game in which each player prefers shirking to working in the absence of exogenous enforcement and can bribe those assigned to monitor him. I find that an optimally designed monitoring structure must have players arranged in a core-periphery network, with a small group of heavily monitored players who monitor all the others. In this network, a perfect Bayesian equilibrium (PBE) is supported in which shirking is prevented, bribery among the players ceases and total monitoring costs are minimized. Furthermore, the efficiency of this core-periphery structure is robust under different cost assumptions and monitoring schedules. In addition, the spread of bribery can be prevented as long as all the “core” players do not collude.

Lecture Notes on the Dynamic Provision of Discrete Public Goods

These lecture notes provide an introduction to dynamic public good provision games. These games can be used to model situations in which a group of agents collaborate to complete a project, or computer scientists developing open source software, or individuals contributing to a fundraising campaign. These notes are targeted to advanced masters' of doctoral students.

Risk in payoff-equivalent appropriation and provision games

Probabilistic risk is examined within appropriation and provision games. Using a menu design, subjects make decisions in multiple one-shot situations where the individual return or the group return is a random variable. Adding risk over the benefits of cooperation is found to significantly affect subjects’ decisions only in situations in the provision game type where the individual return is probabilistic. In those decision situations, cooperation increases.

Asylum Providers: Hawks or Doves?

I examine the noncooperative equilibrium of an asylum provision game in which asylum is an international public good. I show the game can generate multiple equilibria similar to those of the hawk-dove game; the hawkish country is less open to asylum seekers than the dovish is. An inefficient equilibrium is characterized by an underprovision, and a Pareto improvement brings the acceptance of more asylum seekers. I suggest the hawk could and would lead the dove to achieve a Pareto-improving international agreement if the hawk is made to honor the agreement. A non-interfering way to increase asylum provision is to ensure against the breach of such a voluntarily reachable agreement.

INFORMATION VALUE UNDER DEMAND UNCERTAINTY AND ENDOGENOUS MARKET LEADERSHIP

In an oligopoly model with firms choosing to produce in one of two periods, we identify the circumstance under which a firm's having early information regarding stochastic demand results in market leadership. High demand volatility leads to Stackelberg competition with the information‐advantaged firm leading. In the N‐firm case an equilibrium with multiple leaders and multiple followers emerges endogenously. In a duopoly information acquisition game we identify conditions that determine whether neither, one, or both firms will pay to acquire early information and note that one firm's obtaining early information may generate a positive externality benefitting its competitor. Both symmetric and asymmetric outcomes are possible and Stackelberg market leadership may occur in equilibrium, but only when firms have different costs of information. Our finding that an information advantage may convey leadership which then affects the value of information to the players applies to other settings exhibiting first‐mover advantage such as certain public good provision games. (JEL C72, D82, L13)

Community projects: an experimental analysis of a fair implementation process

We define and experimentally test a public provision mechanism that meets three basic ethical requirements and allows community members to influence, via monetary bids, which of several projects is implemented. For each project, participants are assigned personal values, which can be positive or negative. We provide either public or private information about personal values. This produces two distinct public provision games, which are experimentally implemented and analyzed for various projects. In spite of the complex experimental task, participants do not rely on bidding their own personal values as an obvious simple heuristic whose general acceptance would result in fair and efficient outcomes. Rather, they rely on strategic underbidding. Although underbidding is affected by projects’ characteristics, the provision mechanism mostly leads to the implementation of the most efficient project.

Voluntary Participation and Provision of Public Goods in Large Finite Economies

AbstractWe consider a public good provision game with voluntary participation. Agents participating in the game provide a public good and pay the fees according to a mechanism (allocation rule), while nonparticipants can free‐ride on the participants. We examine how the equilibrium public good provision level is affected by enlarging the population of an economy. We introduce a condition for an allocation rule, the asymptotic uniform continuity in replication (AUCR), which requires that small changes in the population must yield only small changes in the public good provision and which is satisfied by many mechanisms. We show that under AUCR, the equilibrium level of the public good converges to zero as the economy is replicated in the sense of Milleron.

Provision versus Appropriation in Symmetric and Asymmetric Social Dilemmas

Social dilemmas characterize decision environments in which individuals' exclusive pursuit of their own material self‐interest can produce inefficient allocations. Social dilemmas are most commonly studied in provision games, such as public goods games and trust games, in which the social dilemma can be manifested in foregone opportunities to create surplus. Appropriation games are sometimes used to study social dilemmas that can be manifested in destruction of surplus, as is typical in common‐pool resource extraction games. A central question is whether social dilemmas are more serious for inhibiting creation of surplus or in promoting its destruction. This question is addressed in this study with an experiment involving three pairs of payoff‐equivalent provision and appropriation games. Some game pairs are symmetric, whereas others involve asymmetric power relationships. We find that play of symmetric provision and appropriation games produces comparable efficiency. In contrast, power asymmetry leads to significantly lower efficiency in an appropriation game than in a payoff‐equivalent provision game. This outcome can be rationalized by reciprocal preference theory but not by models of unconditional social preferences.

Contests and the Private Provision of Public Goods

The private provision of public goods suffers from two potential types of efficiency failures: non-optimal output levels of the public good (quantity problem) and an inefficient mix of contributors and non-contributors (sorting problem). Embedding the provision game into a contest that rewards larger contributions by a higher probability of winning a prize may remedy these failures. Applications include tenure decisions at universities, electoral competition among politicians, or incentives in teams. We characterize the general structure of contests that support efficient allocations. In general, efficiency requires a negative relationship between prize and the decisiveness of the contest. We illustrate our findings with the example of Tullock-type contests.

Contests and the Private Production of Public Goods

The private provision of public goods generally suffers from two types of efficiency failures: sorting problems (the wrong individuals contribute) and quantity problems (an inefficient amount is provided). Embedding the provision game into a contest that rewards larger contributions with higher probabilities of winning a prize may remedy such failures. Applications include tenure decisions at universities, electoral competition among politicians, etc. We identify a tradeoff between the value of the prize and the decisiveness of the contest. High‐powered incentives in contests may cause an overprovision of the public good or wasteful participation of unproductive individuals in the contest.

All but one free ride when wealth effects are small

Quasilinear preferences on a public good and a numeraire good are limits of preferences where both goods are normal. The set of equilibria of the voluntary contribution (or private provision) game is easily characterized under quasilinearity by: top valuators aggregately contribute their common stand-alone contribution, whereas non-top valuators contribute nothing. Because, as long as preferences are randomly selected, there will typically be a single top valuator, it follows that, typically, the equilibrium is unique, with all players but one contributing nothing, hence “free riding” in the sense of the ordinary English usage of the expression. The upper-hemicontinuity of the Nash equilibrium correspondence implies that this is also the case when both goods are strictly normal, but the wealth effects on the public good are small.