A foundation for strategic agenda voting

We offer complete characterizations of the equilibrium outcomes of two prominent agenda voting institutions that are widely used in the democratic world: the amendment, also known as the Anglo-American procedure, and the successive, or equivalently the Euro-Latin procedure. Our axiomatic approach provides a proper understanding of these voting institutions, and allows comparisons between them, and with other voting procedures.     

The welfare consequences of strategic behaviour under approval and plurality voting

This paper studies the welfare consequences of strategic behaviour under approval and plurality voting by comparing the utilitarian efficiencies obtained in simulated voting under two behavioural assumptions: expected utility-maximising behaviour and sincere behaviour. Under approval voting utilitarian efficiency is relatively high irrespective of the behavioural assumption, and under the plurality rule strategic voting significantly increases utilitarian efficiency.     

Non-computability of competitive equilibrium

Summary. We provide a “computable counterexample” to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a “computable counterexample” to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]). Received: September 9, 1997; revised version: December 17, 1997     

Unsettling aspects of voting theory

Summary. Voting procedures are known to be plagued with a variety of difficulties such as strategic voting, or where a voter is rewarded with a better election outcome by not voting, or where a winning candidate can lose by receiving more support. Once we know that these problems can occur, the next objective should be to completely understand how, why, and where they arise. Namely, for each election procedure, the new goal is to determine when such problems can occur, all voter types who can cause these difficulties, and the actions they must take. This paper develops an easily used approach to handle all of these issues for standard voting methods. New intuitive explanations for these various oddities follow from this approach. Received: August 14, 2002 ; revised version: September 4, 2002 RID="*" ID="*"My thanks to Richard Barrett and, in particular, to Hannu Nurmi for corrections, several useful comments, and suggestions they made about earlier versions. Also, my thanks to a referee for calling some excellent references to my attention. An earlier draft was presented at the 2002 Public Choice Society meeting. This research was supported by an NSF grant.     

Cognitive ability and strategic sophistication

In three experiments we examine the extent to which strategic sophistication (i.e., inductive reasoning, iterative dominance and level-k thinking) is determined by broader cognitive skills. In the first experiment we replicate previous results showing strong associations between cognitive ability and sophistication in a game of iterative dominance and show that similar results arise in a game requiring induction. In the second two experiments we extend the literature in new directions. In Experiment 2 we modify the games to better capture participantsʼ ability to reason inductively and predict the sophistication of others and, again, find strong associations between cognitive ability, measured using a common IQ test, and sophistication. In Experiment 3 we examine more closely the causal nature of the relationship between cognitive ability and sophistication. We use a standard tool from cognitive psychology to randomly shock the cognitive ability of participants and show that this significantly affects game performance.     

Promises,policies and pocketbook voting

Do voters respond to political parties׳ promises or to their past actions? We use a suitable sequence of events in Swedish politics to provide the first answer to this question. In the 1994 election campaign the Social Democrats proposed major cuts in transfers to parents with young children, whereas in the 1998 campaign they promised to increase transfers. The Social Democrats won both elections and delivered on both promises. Using voting among parents with slightly older children as counterfactual, we find that voters with young children responded markedly to economic promises rather than to implemented policies.     

Robustness to strategic uncertainty

We introduce a criterion for robustness to strategic uncertainty in games with continuum strategy sets. We model a player's uncertainty about another player's strategy as an atomless probability distribution over that player's strategy set. We call a strategy profile robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in which every player's strategy is optimal under his or her uncertainty about the others. When payoff functions are continuous we show that our criterion is a refinement of Nash equilibrium and we also give sufficient conditions for existence of a robust strategy profile. In addition, we apply the criterion to Bertrand games with convex costs, a class of games with discontinuous payoff functions and a continuum of Nash equilibria. We show that it then selects a unique Nash equilibrium, in agreement with some recent experimental findings.     

The partially cursed and the analogy-based expectation equilibrium

Recent literature has established a link between the fully cursed equilibrium and the analogy-based expectation equilibrium. In this note, even the partially cursed equilibrium is shown to correspond to an analogy-based expectation equilibrium.     

Arbitrage and equilibrium in strategic security markets

Summary. In view of the fundamental price taking hypothesis, arbitrage is never compatible with equilibrium in Walrasian markets because the existence of an arbitrage opportunity in a competitive situation always leads to unbounded arbitrage activity. In strategic markets however, the mere effort of individuals to profit alters market clearing prices and thus distorts arbitrage opportunities as well. This observation suggests a different relationship between arbitrage and equilibrium, than in the competitive model. Indeed, we show that in such markets a spread between the cost of a portfolio and its returns is compatible with equilibrium. We provide an example of an equilibrium where a resourceless individual holds a portfolio with zero cost and positive return in every state. We further demonstrate via an asymptotic result, that no arbitrage is intimately related to price taking behaviour.Received: 8 September 2001, Revised: 6 March 2003, JEL Classification Numbers: G12, D4, D5, D52. Correspondence to: Leonidas C. Koutsougeras     

Beauty contest,bounded rationality,and sentiment pricing dynamics

We present a dynamic asset pricing model that incorporates investor sentiment, bounded rationality and higher-order expectations to study how these factors affect asset pricing equilibrium. In the model, we utilize a two-period trading market and investors make decisions based on the heterogeneous expectations principle and the “sparsity-based bounded rational” sentiment. We find that bounded rationality results in mispricing and reduces it in next period. Investor sentiment produces more significant effects than private signals, optimistic investor sentiment increases hedging demand, thus causing prices to soar. Higher-order investors are more rational and attentive to the strategies of other participants rather than private signals. This model also derives the dampening effect of higher-order expectations to price volatility and the heterogeneity expectation depicts inconsistent investor behavior in financial markets. In the model, investors' expectations about future price is distorted by their sentiment and bounded rationality, so they obtain a biased mean from the signal extraction.     

A spectrum of equilibration processes in game theory

In game theory, four dynamic processes converging towards an equilibrium are distinguished and ordered by way of agents' decreasing cognitive capacities. In the eductive process, each player has enough information to simulate perfectly the others' behavior and gets immediately to the equilibrium. In epistemic learning, each player updates his beliefs about others' future strategies, with regard to their sequentially observed actions. In behavioral learning, each player modifies his own strategies according to the observed payoffs obtained from his past actions. In the evolutionary process, each agent has a fixed strategy and reproduces in proportion to the utilities obtained through stochastic interactions. All along the spectrum, longer term dynamics makes up for weaker rationality, and physical relations substitute for mental interactions. Convergence, if any, is towards an always stronger equilibrium notion and selection of an equilibrium state becomes more sensitive to context and history. The processes can be mixed if associated to different periods, agents or mechanisms and deepened if obtained by formal reasoning principles.     

Sunspot-like equilibria in an overlapping generations economy with strategic interactions

In this paper I analyze the effect of market uncertainty in an overlapping generations economy with strategic interactions among agents. I demonstrate the existence of sunspot-like equilibria, in which arbitrarily small amounts of intrinsic uncertainty in agents’ offers generate large fluctuations in equilibrium bids and prices. I would like to express my gratitude to Stephen Spear for his guidance during the realization of this project. I thank an anonymous referee for providing insightful comments and suggestions. I have benefited from comments by Alexander Elbittar, Cesar Guerrero, and Vivek Ramachandran.     

Policy Consequences of Multiple Equilibria and the Indeterminacy of Economic Outcomes in a Boundedly Rational World: Closing the System with Non-Economic Variables1

In the conventional economic wisdom, the notion of unique equilibria that are efficient and Pareto optimal dominates the modeling discourse. Hebert Simon proposed an alternative analytical framework where the notion of multiple and sustainable equilibria is critical. Multiple equilibrium is the crucial stylized fact of economic life that requires better understanding and modeling. Of particular significance, Simon touched on the importance of institutions and differential power relationships in affecting economic outcomes. But this modeling approach was not well developed by Simon. Following from his contributions, further develop the notion of multiple equilibria especially in the realm of production with an emphasis on x-efficiency theory. I bring to bear the importance of institutional parameters (including power relationships), culture, norms, ethics, and moral sentiments to the determination of economic outcomes. In the model developed here, boundedly rational decision-makers’ choices are contextualized and constrained by complex environmental factors. No one choice is either inevitable or economically efficient. A multiplicity of outcomes is possible and sustainable inclusive of those that are suboptimal. Much depends on individual preferences and institutional design. This has significant implication for institutional design and policy.     

Learning by trial and error

A person learns by trial and error if he occasionally tries out new strategies, rejecting choices that are erroneous in the sense that they do not lead to higher payoffs. In a game, however, strategies can become erroneous due to a change of behavior by someone else. We introduce a learning rule in which behavior is conditional on whether a player experiences an error of the first or second type. This rule, called interactive trial and error learning, implements Nash equilibrium behavior in any game with generic payoffs and at least one pure Nash equilibrium.     

Public goods,voting, and growth

We study a parametric politico‐economic model of economic growth with productive public goods and public consumption goods. The provision of public goods is funded by a proportional tax. Agents are heterogeneous in their initial capital endowments, discount factors, and the relative weights of public consumption in overall private utility. They vote on the shares of public goods in gross domestic products (GDP). We propose a definition of voting equilibrium, prove the existence and provide a characterization of voting equilibria, and obtain a closed‐form solution for the voting outcomes. Also we introduce a “fictitious” representative agent and interpret the outcome of voting as a choice made by a central planner for his benefit. Finally, we undertake comparative static analysis of the shares of public goods in GDP and of the rate of balanced growth with respect to the discount factors and the preferences for public consumption. The results of this analysis suggest that the representative‐agent version of our model is capable of capturing the interaction between many voting heterogeneous agents only if the heterogeneity is one‐dimensional.     

Nash equilibrium without mutual knowledge of rationality

Summary. In a Nash equilibrium, players' rationality is mutual knowledge. However, both intuition and experimental evidence suggest that players do not know for sure the rationality of opponents. This paper proposes a new equilibrium concept, cautious equilibrium, that generalizes Nash equilibrium in terms of preferences in two person strategic games. In a cautious equilibrium, players do not necessarily know the rationality of opponents, but they view rationality as infinitely more likely than irrationality. For suitable models of preference, cautious equilibrium predicts that a player might take a “cautious” strategy that is not a best response in any Nash equilibrium. Received: January 28, 1998; revised version October 2, 1998     

Revisiting games of incomplete information with analogy-based expectations

This paper studies the effects of analogy-based expectations in static two-player games of incomplete information. Players are assumed to be boundedly rational in the way they forecast their opponent's state-contingent strategy: they bundle states into analogy classes and play best-responses to their opponent's average strategy in those analogy classes. We provide general properties of analogy-based expectation equilibria and apply the model to a variety of well known games. We characterize conditions on the analogy partitions for successful coordination in coordination games under incomplete information [Rubinstein, A., 1989. The electronic mail game: Strategic behavior under ‘almost common knowledge’. Amer. Econ. Rev. 79, 385–391], we show how analogy grouping of the receiver may facilitate information transmission in Crawford and Sobel's cheap talk games [Crawford, V.P., Sobel, J., 1982. Strategic information transmission. Econometrica 50, 1431–1451], and we show how analogy grouping may give rise to betting in zero-sum betting games such as those studied to illustrate the no trade theorem.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.     

Extensive-form games and strategic complementarities

I prove the subgame-perfect equivalent of the basic result for Nash equilibria in normal-form games of strategic complements: the set of subgame-perfect equilibria is a nonempty, complete lattice—in particular, subgame-perfect Nash equilibria exist. For this purpose I introduce a device that allows the study of the set of subgame-perfect equilibria as the set of fixed points of a correspondence. My results are limited because extensive-form games of strategic complementarities turn out—surprisingly—to be a very restrictive class of games.     

Improving the performance of an economic system: Controlling chaos

In this paper we use a simple model of evolutionary market dynamics to illustrate how chaotic behavior can be controlled by making small changes in a parameter that is accessible to the decision makers. This approach is commonly referred to as `targeting' – one can easily switch from a chaotic evolution of the market to any desired regular motion. We show that complex dynamics leads to inferior performance in our model and that an application of such a correction mechanism by the decision makers of the firms yields a considerable improvement in the system's economical properties in terms of profits and profitability. We present numerical simulations in order to illustrate the effectiveness of this method.