Topological games at Princeton, a mathematical memoir

The games of the title are “Nash” (or Hex), “Milnor” (or Y), “Shapley” (or Projective Plane) and “Gale” (or Bridg-It) all of which were discovered (or re-discovered) in Princeton in 1948–1949. After giving the basic topological connections, I will discuss more recent ramifications related to computational complexity theory. A recurrent theme will be non-constructive proofs, or how we can know something can be done without having the slightest idea of how to do it.     

The Art of Scenarios and Strategic Planning: Tools and Pitfalls

The term strategy has been misused and even abused. Worse, the word scenario is often confused with strategy to the point that clarification is needed if we are to understand one another. As a prolongation of the work done by the Rand Corporation in the 1960s, strategic planning, management and prospective approaches have been developed to help organizations master change. Over the past 25 years, we have contributed by creating or further developing various methodologies and procedures such as the Mactor and MICMAC methods for use in scenario building. These tools are doubly powerful in that they stimulate the imagination, reduce collective biases, and promote appropriation. One of the main functions of the strategic futures exercise is to eliminate two errors that we usually describe as the “hammer's risk” and the “nail's dream.” In other words, we forget what a hammer's function is when staring at a nail (the nail's dream) or we know how to use a hammer and imagine that every problem is like a nail (the hammer's risk). In our case, we strive to give simple tools that may be appropriated. However, these simple tools are inspired by intellectual rigor that enables one to ask the right questions. Of course, these tools do not come with a guarantee. The natural talent, common sense, and intuition of the futurist also count!     

Choquet Rationality

Consider a decision problem under uncertainty for a decision maker with known (utility) payoffs over prizes. We say that an act is Choquet (Shafer, Bernoulli) rational if for some capacity (belief function, probability) over the set of states, it maximizes her “expected” utility. We show that an act may be Choquet rational without being Bernoulli rational, but it is Choquet rational if and only if it is Shafer rational. Journal of Economic Literature Classification Numbers: C72, D81.     

Eliciting Preferences to Assign Positions and Compensation

We describe strategy-proof rules for economies where an agent is assigned a position (e.g., a job) plus some of a divisible good. For the 2-agent–2-position case we derive a robust characterization. For the multi-agent–position case, many “arbitrary” such rules exist, so we consider additional requirements. By also requiring coalitional strategy-proofness or nonbossiness, the range of a solution is restricted to the point that such rules are not more complex than those for the Shapley–Scarf housing model (no divisible good). Third, we show that essentially only constant solutions are immune to manipulations involving “bribes.” Finally, we demonstrate a conflict between efficiency and strategy-proofness. The results extend to models (without externalities) in which agents share positions. Journal of Economic Literature Classification Numbers: C72, D70.     

“Constitutionalizing” the corporation

To become effective instruments in the attainment of a sustainable society, corporations should have their constitutional status settled. Thus far, mainly by Supreme Court decisions, corporations have an uncertain status. They are “persons” under the Constitution and have certain rights; but unlike natural persons, they do not have concomitant constitutional duties. Corporations should be viewed as “private” governments exercising substantial power in society. They are, however, considered to be associations of individuals rather than divisions of society. The need is to legitimate their governing power by “constitutionalizing” them. That can be done by corporations accepting, or having imposed upon them, two principal constitutional duties. First, means should be developed whereby corporate officers routinely take the general good into account. That duty could be implemented by making “social impact statements,” analogous to but broader than the familiar environmental impact statements, before making important corporate decisions. Secondly, as “sociological communities,” corporate officers wield considerable power over members of those communities. A bill of rights similar to the Constitution's Bill of Rights is recommended so as to make corporate power that is necessary for achievement of societal goals as tolerable and decent as possible. Acceptance of those duties would make corporations parts of, not separate from, the greater corporation called society. They would be private, profit-making entities with a definite public function. Preferably, the duties should be voluntarily accepted. Congress, however, has undoubted constitutional power to impose both, should it so desire.     

Influence and inefficiency in the internal capital market

I model inefficient resource allocations in M-form organizations due to influence activities by division managers that skew capital budgets in their favor. Corporate headquarters receives two types of signals about investment opportunities: private signals that can be distorted by managers, and public signals that are undistorted but noisy. Headquarters faces a tradeoff between the cost of attaining an accurate private signal and the value of the information the signal provides. In contrast to existing models of “socialism” in internal capital markets, I show that investment sensitivity to Tobin's Q is higher than first-best in firms where division managers hold equity (a result consistent with evidence presented in Scharfstein, 1998). When managers face high private costs from distorting information (equity holdings), headquarters may commit to investment contracts that place “too little” weight on private signals and “too much” weight on public signals (i.e. Q). This result has implications for managers in the design of capital budgeting processes and incentive compensation systems.     

Unfolding Social Hierarchies

Consider a large population of finitely-lived agents organized into n different hierarchical levels. Every period, all those placed at each level are randomly matched to play a given symmetric game. Based on the resulting outcome, a ρ-fraction of agents who (within their own level) attain the highest payoffs are promoted upwards. On the other hand, newcomers replacing those who die every period enter at the lowest level and choose irreversibly the strategy to be played for the rest of their life. This choice is made, with some noise, by imitating one of the strategies adopted at the highest level.  In this setup, the unique long-run behavior of the system is fully characterized for the whole class of 2×2 coordination games and two alternative variations of the model. The results crucially depend on the key “institutional” parameters ρ and n. In particular, it is shown that inefficient behavior prevails in the long run (even when risk-dominated) if promotion is only mildly selective—high ρ—and the social system is quite hierarchical—large n. In a stylized manner, these parameter conditions may be viewed as reflecting a sort of institutional deficiency that impairs economic performance. Journal of Economic Literature Classification Numbers: C70, C72, C73, D72.     

Rational Choice and the Condorcet Jury Theorem

In a recent paper, Austen-Smith and Banks (1996,Amer. Polit. Sci. Rev.90, 34–45), criticize the current literature on the Condorcet jury theorem as neglecting the behavioral underpinnings of decision-making. They leave open the question whether allowing mixed strategies would sustain the conclusions of the Condorcet jury theorem. In this paper, it is shown that these conclusions can hold in equilibrium. In other words, “a rational choice foundation for the claim that majorities invariably ‘do better’ than individuals” is derived. (Journal of Economic LiteratureClassification Number: D72.     

Contracts and externalities: How things fall apart

A single principal interacts with several agents, offering them contracts. The crucial assumption of this paper is that the outside-option payoffs of the agents depend positively on how many uncontracted or “free” agents there are. We study how such a principal, unwelcome though he may be, approaches the problem of contract provision to agents when coordination failure among the latter group is explicitly ruled out. Two variants are considered. When the principal cannot re-approach agents, there is a unique equilibrium, in which contract provision is split up into two phases. In phase 1, simultaneous offers at good (though varying) terms are made to a number of agents. In phase 2, offers must be made sequentially, and their values are “discontinuously” lower: they are close to the very lowest of all the outside options. When the principal can repeatedly approach the same agent, there is a multiplicity of equilibria. In some of these, the agents have the power to force delay. They can hold off the principal's overtures temporarily, but they must succumb in finite time. In both models, despite being able to coordinate their actions, agents cannot resist an “invasion” by the principal and hold to their best payoff. It is in this sense that “things [eventually] fall apart”.     

A prospective on macrocybernetic process management systems

In an editorial in the February 1996 issue of Technological Forecasting and Social Change Professor Linstone noted that “the rapid pace of technology has not been matched by the pace of human change.” Were we to drop our perspective a bit lower, a similarly troublesome imbalance within technology itself becomes apparent: the rapid rate of increase in the complexity of process-related technologies relative to the much slower rate of increase in the sophistication of process control systems. The conclusion at which most technological forecasts seem to arrive is that there will be a continuation—perhaps even an acceleration—of the trend toward more intricate and sweepingly extensive processes (production-related and otherwise). If so, there is the specter of a steadily increasing shortfall between requirements and capabilities, and hence the likelihood of even grander technological embarrassments. This article considers two ways in which this shortfall might be kept in check. Increases in the intricacy of processes can be met, and to a considerable extent are already being met, by exchanging conventional process control facilities for enhanced alternatives. Less certain is how expansions of project scope might best be accommodated. One possibility is to consider exchanging process control systems for broader-purview process management systems. Hence the focus in this article is on prospects for the development of macrocybernetic constructs.     

Concatenate coordination and mutual coordination

We tell of the evolving meaning of the term coordination as used by economists. The paper is based on systematic electronic searches (on “coord,” etc.) of major works and leading journals. The term coordination first emerged in professional economics around 1880, to describe the directed productive concatenation of factors or activities within a firm. Also, transportation economists used the term to describe the concatenation of routes and trips of a transportation system. These usages represent what we term concatenate coordination. The next major development came in the 1930s from several LSE economists (Hayek, Plant, Hutt, and Coase), who extended that concept beyond the eye of any actual coordinator. That is, they wrote of the concatenate coordination of a system of polycentric or spontaneous activities. These various applications of concatenate coordination prevailed until the next major development, namely, Thomas Schelling and game models. Here coordination referred to a mutual meshing of actions. Game theorists developed crisp ideas of coordination games (like “battle of the sexes”), coordination equilibria, convention, and path dependence. This “coordination” was not a refashioning, but rather a distinct concept, one we distinguish as mutual coordination. As game models became more familiar to economists, it was mutual coordination that economists increasingly had in mind when they spoke of “coordination.” Economists switched, so to speak, to a new semantic equilibrium. Now, mutual coordination overshadows the older notion of concatenate coordination. The two senses of coordination are conceptually distinct and correspond neatly to the two dictionary definitions of the verb to coordinate. Both are crucial to economics. We suggest that distinguishing between the two senses can help to clarify “coordination” talk. Also, compared to talk of “efficiency” and “optimality,” concatenate coordination allows for a richer, more humanistic, and more openly aesthetic discussion of social affairs. The narrative is backed up by Excel worksheets that report on systematic content searches of the writings of economics using the worldwide web and, using JSTOR, of Quarterly Journal of Economics, Economic Journal, Journal of Political Economy, American Economic Review, and Economica.     

A Proof of Calibration via Blackwell's Approachability Theorem

Over the past few years many proofs of the existence of calibration have been discovered. Each of the following provides a different algorithm and proof of convergence: D. Foster and R. Vohra (1991, Technical Report, University of Chicago), (1998, Biometrika85, 379–390), S. Hart (1995, personal communication), D. Fudenberg and D. Levine (1999, Games Econ. Behavior29, 104–130), and S. Hart and A. Mas-Colell (1997, Technical Report, Hebrew University). Does the literature really need one more? Probably not. But the algorithm proposed here has two virtues. First, it only randomizes between two forecasts that are very close to each other (either p or p + ε). In other words, the randomization only hides the last digit of the forecast. Second, it follows directly from Blackwell's approachability theorem, which shortens the proof substantially. Journal of Economic Literature Classification Numbers: C70, C73, C53.     

Undominated Nash Implementation with Collusion and Renegotiation

This article looks at implementation in economic environments when agents have perfect information about the state of the world, but cannot commit not to renegotiate bad outcomes or to collude against each other. If renegotiation satisfies a weak condition of disagreement point monotonicity, then any Pareto-efficient social choice function can be implemented if there are at least three agents who play undominated Nash equilibria. The mechanism does not use modulo or integer games, has no bad mixed strategy equilibria, and is “bounded.”Journal of Economic LiteratureClassification Number: D71.     

Optimality and Robustness of the English Auction

In Milgrom and Weber's (1982, Econometrica50, 1089–1122) “general symmetric model,” under a few additional regularity conditions, the English auction maximizes the seller's expected profit within the class of all posterior-implementable trading procedures and fails to do so among all interim incentive-compatible procedures in which “losers do not pay.” These results suggest that appropriate notions of robustness and simplicity which imply the optimality of the English auction for a risk-neutral seller must impose “bargaining-like” features on the set of feasible trading mechanisms. Journal of Economic Literature Classification Numbers: D44, D82.     

On the Existence of Stable Roommate Matchings

This paper identifies a condition called “no odd rings” that is sufficient for the existence of stable roommate matchings in the weak preferences case. It shows that the process of allowing randomly chosen blocking pairs to match converges to a stable roommate matching with probability one as long as there are no odd rings. This random-paths-to-stability result generalizes that of Roth and Vande Vate (1990, Econometrica58, 1475–1480) and may not hold if there are odd rings. The “no odd rings” condition can also be used to prove a number of other sufficient conditions that are more economically interpretable. Journal of Economic Literature Classification Numbers: C78, D71.     

Is man doomed to progress?

This paper is dedicated to the empirical exploration of the welfare effect of expectations and progress per se. Using 10 waves of the Russian Longitudinal Monitoring Survey (RLMS), a panel household survey rich in subjective variables, the analysis suggests that for a given total stock of inter-temporal consumption, agents are more satisfied with an increasing time profile of consumption: they seem to have a strong “taste for improvement”. This contributes to qualify the “Easterlin paradox” that income growth does not make people happy.     

Political Competition, Rent Seeking and the Choice of Environmental Policy Instruments: Comment

In this comment, I analyze Damania's political economy model (Environmental and Resource Economics 13: 415–433, 1999), correcting some flaws and clarifying some ambiguities. I arguethat the political parties are identical at the outset of the game. Onlyafter the parties have chosen the instrument (standards or taxation) and thestrictness of environmental policy do the environmentalists and thepolluting firms know which party to support in the election campaign. Inequilibrium, both parties choose the same platform, so that both have anequal probability of winning the election.     

Minimizing Regret: The General Case

In repeated games with differential information on one side, the labelling “general case” refers to games in which the action of the informed player is not known to the uninformed, who can only observe a signal which is the random outcome of his and his opponent's action. Here we consider the problem of minimizing regret (in the sense first formulated by J. Hannan (1956, in Contributions to the Theory of Games, Vol. III, Annals of Mathematics Studies, Vol. 39, Princeton, NJ: Princeton Univ. Press.) when the information available is of this type. We give a simple condition describing the approachable set. Journal of Economic Literature Classification Number: D81, D82, D83.     

Non-Walrasian Labor Markets and Real Business Cycles

The standard real business cycle literature mainly focuses on Walrasian models designed to fit the U.S. institutional framework. Differences between the United States and Europe, mostly evident in the labor market, suggest that a purely Walrasian model may be inappropriate for the study of European business cycles. I present a stochastic version of the dynamic general equilibrium model of Daveri and Maffezzoli (2000, “A Numerical Approach to Fiscal Policy, Unemployment and Growth in Europe,” Econometrics and Applied Economics Working Paper 2000-4, IEP, Università Bocconi), where unemployment is generated by monopolistic unions, and calibrate it to reproduce several long-run features of the Italian and U.S. economies. This framework is then compared with an indivisible labor model built on Hansen (1985, Journal of Monetary Economics16, 309–328) and Rogerson and Wright (1988, Journal of Monetary Economics22, 501–515). I focus on the impulse response functions, the standard business cycle statistics, and the ability to reproduce the cyclical components of the main macroeconomic variables. The main results are as follows: (i) the impulse response functions of the monopoly union (MU) model show a higher degree of overall persistence; (ii) the business cycle statistics are similar; (iii) the MU model enjoys a statistically significant advantage in reproducing the Italian business cycle, but not that of the United States. Journal of Economics Literature Classification Numbers: E32, E24, J23, J51.     

Determinants of demand for green products: An application to eco-label demand for fish in Europe

In this paper, we confront the theoretical motivations of the consumption of eco-friendly products and the factors influencing the European perceptions regarding the fact that “fish caught using an environmentally friendly technique may carry a special label”. We take advantage of the recent integration of non-economic elements in the microeconomic analysis of consumers' behavior in order to highlight the factors leading to their demand for green products. Thanks to an original European survey on seafood product carried out on more than 5000 consumers, we test the influence of intrinsic motivation, information, localization and socio-economic factors on the demand for an eco-label for fish.Our results show a significant connection between the desire for eco-labeling and seafood features, especially the freshness of the fish, the geographical origin of the fish and the wild vs farmed origin of the fish. Moreover, we prove the major role played by the fish price. We also demonstrate that the ecological issue regarding fisheries is highly connected to consumer information, intrinsic motivation and socio-economic status: the typical “green fish consumer” is a young woman, well educated, well informed on the state of marine resources and not very trusting of the regulation of the fisheries. Consumers who are aware of the importance of marine resource preservation have the same profile.