On the consistency of conjectures with public goods

This note addresses Sugden's criticisms, levelled against our Non-Nash theory for public goods. In particular, we argue that our previous exercise was not to present a theory of public goods that could escape the voluntary contribution problem by relaxing Nash conjectures. Rather, our non-Nash model was merely an analytical exercise, meant to encompass a widevariety of behaviour. This note also indicates when positive conjectures might be realistic and, therefore, potentially consistent. Finally, we extend our specific example to include negative, zero, and positive conjectures.     

Efficiency and stability of sampling equilibrium in public goods games

Most models of social preferences and bounded rationality that are effective in explaining efficiency‐increasing departures from equilibrium behavior cannot easily account for similar deviations when they are efficiency‐reducing. We show that the notion of sampling equilibrium, subject to a suitable stability refinement, can account for behavior in both efficiency‐enhancing and efficiency‐reducing conditions. In particular, in public goods games with dominant strategy equilibria, stable sampling equilibrium can involve the play of dominated strategies with positive probability both when such behavior increases aggregate payoffs (relative to the standard prediction) and when it reduces aggregate payoffs. The dominant strategy equilibrium prediction changes abruptly from zero contribution to full contribution as a parameter crosses a threshold, whereas the stable sampling equilibrium remains fully mixed throughout. This is consistent with the available experimental evidence.     

A further look at consistent conjectures and private provision of public goods

A model of private provision of a public good under conjectural variations is discussed and the rule for a symmetric consistent conjectures equilibrium (CCE) derived. It is shown that in a number of reasonable cases symmetric CCEs fail to exist in economies with identical individuals, while there may exist asymmetric ones. The relevance of these results for the use of the conjectural variations approach in public good theory is then discussed together with some suggestions for further research.     

Credible assignments can improve efficiency in laboratory public goods games

This paper reports an experiment investigating how assignments improve economic efficiency in a modified version of the standard voluntary-contributions mechanism. The experiment uses a non-binding message that makes common information assignments in the repeated game. A credible assignment is one actually followed by the participants. It turns out to be difficult to credibly assign the symmetric efficient outcome in four person cohorts, but we did discover one assignment that was credible in the last match of the evolutionary repeated game.     

The benefits of voluntary leadership in experimental public goods games

We study the effects of voluntary leadership in experimental public goods games when each group member can volunteer to contribute before the other members. We find that voluntary leadership increases contributions significantly, compared to a treatment where leadership is enforced exogenously.     

Rational responses and rational conjectures

This paper utilizes a pure-trade imperfect-competition model and discusses the rationality problem arising from the fact that agents have to make conjectures about the markets to set prices optimally. The objective is to show that there may be inefficient allocations with the agents behaving rationaly. In the same context Hahn (Rev. Econ. Stud.45 (1978), 1–17) proposed a notion of rationality under which the existence results obtained were negative. This paper argues that Hahn's is a strong notion of rationality that requires the mechanism to be incentive compatible. Thus, an alternative notion that refers exclusively to the rationality of the conjectures is proposed, and positive results on existence obtained.     

Consistent conjectures and voluntary contributions to public goods: why the conventional theory does not work

The conventional theory of voluntary contributions to public goods assumes that each person maximises his utility taking other people's behaviour as given (Nash conjectures). It is now coming to be recognised that this theory is inconsistent with observed behaviour. This paper argues that the problems of the theory are compounded — and not, as some economists have argued, resolved — by relaxing the assumption of Nash conjectures. If individuals' conjectures are consistent, each person will hold the (correct) belief that other people's contributions are inversely related to his own. Under most reasonable assumptions, equilibrium is a state in which no-one contributes anything.     

Mindreading and endogenous beliefs in games

We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We show in particular that those beliefs need not be ratifiable, and therefore that rational players can form action-dependent beliefs.     

Estimating the causal effect of beliefs on contributions in repeated public good games

We use instrumental variables for estimating the causal effect of beliefs on contributions in repeated public good games. The effect is about half as large as suggested by ordinary least squares. Thus, we present evidence that beliefs have a causal effect on contributions, but also that beliefs are endogenous. We compare the causal, belief-based model of contributions to alternative models based on matching the previous contributions of others and responding to one’s deviation from the average in the previous round. The causal, belief-based model performs well, indicating that beliefs have a central role in determining contributions.     

Evolutionarily stable conjectures and other regarding preferences in duopoly games

We study the evolutionary selection of conjectures in duopoly games when players have other regarding preferences, i.e. preferences over payoff distributions. In both the Cournot and Bertrand duopoly games, the consistent conjectures are independent of other regarding preferences. Both duopoly games have evolutionarily stable conjectures that depend on other regarding preferences but that do not coincide with the consistent conjectures. For increasingly spiteful preferences, the evolutionarily stable conjectures implicate low quantities in the Cournot game and high prices in the Bertrand game, whereas the inverse relationships hold for the consistent conjectures. We discuss our findings in the context of ultimate and proximate causation.     

Technology and public goods

This paper presents a theory of public goods based on production theory where public goods are viewed as inputs to the production process. We examine the pure case of public inputs (no private inputs) as well as the mixed case (private and public inputs). We show how the case of public inputs is related to certain forms of nonjoint production, and we characterize it in terms of variable profit and joint cost functions. Comparative statics results are derived graphically in the two-by-two case.     

Power and public goods

A game-theoretic analysis using the Harsanyi-Shapley nontransferable utility value indicates that the choice of public goods in a democracy is not affected by who has voting rights. This is corroborated by an independent economic argument based on the implicit price of a vote.     

The evolutionary stability of constant consistent conjectures

In the general context of smooth two-player games, this paper shows that there is a close connection between (constant) consistent conjectures in a given game and the evolutionary stability of these conjectures. Evolutionarily stable conjectures are consistent and consistent conjectures are the only interior candidates to be evolutionarily stable. Examples are provided to illustrate the result.     

On eliciting beliefs in strategic games

Several recent studies in experimental economics have tried to measure beliefs of subjects engaged in strategic games with other subjects. Using data from one such study we conduct an experiment where our experienced subjects observe early rounds of strategy choices from that study and are given monetary incentives to report forecasts of choices in later rounds. We elicit beliefs using three different scoring rules: linear, logarithmic, and quadratic. We compare forecasts across the scoring rules and compare the forecasts of our trained observers to forecasts of the actual players in the original experiment. We find significant differences across scoring rules. The improper linear scoring rule produces forecasts closer to 0 and 1 than the proper rules, and these forecasts are poorly calibrated. The two proper scoring rules induce significantly different distributions of forecasts. We find that forecasts by observers under both proper scoring rules are significantly different from the forecasts of the actual players, in terms of accuracy, calibration, and the distribution of forecasts. We also find evidence for belief convergence among the observers.     

Match choice and Ghettoization in evolutionary games

I study how having a choice about who to play affects the conventions that arise in a population playing a 2×2 common interest game. Match choice allows agents playing “fragile but efficient” strategies to isolate themselves, raising their returns but making it harder for outsiders to duplicate their success. When agents are myopic, the second effect dominates: long run play can shift toward either the risk-dominant equilibrium (with common interests in matching) or toward the inefficient equilibrium (with opposing interests in matching). In contrast, when agents are patient, supra-Nash payoffs can be sustained.     

Public goods and public bads

In many empirically relevant situations agents in different groups are affected by the provision of a public characteristic in divergent ways. Whereas for one group it represents a public good, it is a public bad for another group. Applying Cornes and Hartley's aggregative game approach, we analyze a general model in which such contentious public characteristics are present and are provided cooperatively. In particular, we establish neutrality results with respect to redistribution and growth of income, infer the effects of preference changes and coalition formation, and present a technology paradox. Finally, we compare the outcome of voluntary provision of the contentious public characteristic with the Pareto‐optimal solution, highlighting a potential conflict between equity and efficiency in this case.     

Constrained public goods in networks

This paper analyses the private provision of public goods where agents interact within a fixed network structure and may benefit only from their direct neighbours’ provisions. We generalise the public goods in the networks model of Bramoullé and Kranton [J. Econ. Theory 135 (2007), pp. 478–494] to allow for constrained provision. In so doing, we characterise Nash equilibria with no intermediate contributors.     

Revision of conjectures about the opponent’s utilities in signaling games

In this paper we apply the concept of preference conjecture equilibrium introduced in Perea (2005) to signaling games and show its relation to sequential equilibrium. We introduce the concept of minimum revision equilibrium and show how this can be interpreted as a refinement of sequential equilibrium