Computational Complexity and Communication: Coordination in Two–Player Games

The main contribution of this paper is the development and application of cryptographic techniques to the design of strategic communication mechanisms. One of the main assumptions in cryptography is the limitation of the computational power available to agents. We introduce the concept of limited computational complexity, and by borrowing results from cryptography, we construct a communication protocol to establish that every correlated equilibrium of a two–person game with rational payoffs can be achieved by means of computationally restricted unmediated communication. This result provides an example in game theory where limitations of computational abilities of players are helpful in solving implementation problems. More specifically, it is possible to construct mechanisms with the property that profitable deviations are too complicated to compute.     

Corrigendum to “Games With Imperfectly Observable Actions in Continuous Time”

Sannikov (2007) investigated properties of perfect public equilibria in continuous‐time repeated games. This note points out that the proof of Lemma 6, required for the proof of the main theorem (Theorem 2), contains an error in computing a Hessian matrix. A correct proof of Lemma 6 is provided using an additional innocuous assumption and a generalized version of Lemma 5.     

Comment on “Commitment vs. Flexibility”

This comment corrects two results in the 2006 Econometrica paper by Amador, Werning, and Angeletos (AWA), that features a model in which individuals face a trade‐off between flexibility and commitment. First, in contrast to Proposition 1 in AWA, we show that money‐burning can be part of the ex ante optimal contract when there are two states. Second, in contrast to Proposition 2 in AWA, we show that money‐burning can be imposed at the top (in the highest liquidity shock state), even when there is a continuum of states. We provide corrected versions of the above results.     

Corrigendum to “Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples”

Levy (2013) presented examples of discounted stochastic games that do not have stationary equilibria. The second named author has pointed out that one of these examples is incorrect. In addition to describing the details of this error, this note presents a new example by the first named author that succeeds in demonstrating that discounted stochastic games with absolutely continuous transitions can fail to have stationary equilibria.     

Comment on “The Law of Large Demand for Information”

Say that one information structure is eventually Blackwell sufficient for another if, for every large enough n, an n‐sample from the first is Blackwell sufficient (Blackwell (1951, 1954)) for an n‐sample from the second. This note shows that eventual Blackwell sufficiency lies strictly between (one‐shot) Blackwell sufficiency and the ordering of information structures formulated by Moscarini and Smith (2002), and thus offers a new criterion for comparing experiments. A characterization of eventual Blackwell sufficiency in terms of the one‐shot experiments remains an open question.     

Comment on “Constrained Optimization Approaches to Estimation of Structural Models”

We revisit the comparison of mathematical programming with equilibrium constraints (MPEC) and nested fixed point (NFXP) algorithms for estimating structural dynamic models by Su and Judd (2012). Their implementation of the nested fixed point algorithm used successive approximations to solve the inner fixed point problem (NFXP‐SA). We redo their comparison using the more efficient version of NFXP proposed by Rust (1987), which combines successive approximations and Newton–Kantorovich iterations to solve the fixed point problem (NFXP‐NK). We show that MPEC and NFXP are similar in speed and numerical performance when the more efficient NFXP‐NK variant is used.     

Remitting Behaviour of “Temporary” and “Permanent” Migrants: The Case of Greeks in Germany and Australia

This paper makes the point that migrants have different motives for sending remittances and remittance receivers have different claims on migrants' income, depending on whether people move to accumulate capital to improve their living at home after they return — temporary migration — or to start a new life in a foreign country — permanent migration. This hypothesis is empirically tested with data from Greek–German and Greek–Australian migration. The findings attest to the fact that German remittances constitute obligatory income streams to close family at home, while Australian remittances are gifts. Some quantitative estimates of the relative impact of individual factors on remittances are also obtained. Some hints are also given for a changing remitting behaviour of Greek migrants in Germany, along with the changing character of migration in that country.     

Note on “many-sided shadow prices”

It has been previously shown, with the aid of a simple example, that linear programmes may have two different non-negative marginal values at the optimum if the solution is degenerate. It is demonstrated in this note that other marginal values exist which may take negative values.     

On “Black Swans” and “Perfect Storms”: Risk Analysis and Management When Statistics Are Not Enough

Two images, “black swans” and “perfect storms,” have struck the public's imagination and are used—at times indiscriminately—to describe the unthinkable or the extremely unlikely. These metaphors have been used as excuses to wait for an accident to happen before taking risk management measures, both in industry and government. These two images represent two distinct types of uncertainties (epistemic and aleatory). Existing statistics are often insufficient to support risk management because the sample may be too small and the system may have changed. Rationality as defined by the von Neumann axioms leads to a combination of both types of uncertainties into a single probability measure—Bayesian probability—and accounts only for risk aversion. Yet, the decisionmaker may also want to be ambiguity averse. This article presents an engineering risk analysis perspective on the problem, using all available information in support of proactive risk management decisions and considering both types of uncertainty. These measures involve monitoring of signals, precursors, and near‐misses, as well as reinforcement of the system and a thoughtful response strategy. It also involves careful examination of organizational factors such as the incentive system, which shape human performance and affect the risk of errors. In all cases, including rare events, risk quantification does not allow “prediction” of accidents and catastrophes. Instead, it is meant to support effective risk management rather than simply reacting to the latest events and headlines.     

Response to “Revisiting ISO 14000 Diffusion: A New ”Look“ at the Drivers of Certification”

In Corbett and Kirsch (2001), we used a simple regression in an exploratory investigation of drivers of global diffusion of ISO 14000 certification. We found that ISO 9000 certification levels, environmental treaties ratified, and exports as a proportion of GDP were the main significant variables, where the environmental measure may be moderated by GDP per capita. In his replication study, Vastag (2004, in this issue) analyzes the same data using more visual techniques, specifically regression trees, and finds support for the significance of ISO 9000 certification levels and environmental treaties ratified, but not for export‐propensity. Vastag raises a number of relevant methodological issues, to which we add some perspectives here.     

THE TIMING OF LABOR TRANSFERS IN DUAL RESOURCE-CONSTRAINED SYSTEMS: “PUSH” VS. “PULL” RULES*

Altough the dual resource-constrained (DRC) system has been studied, the decision rule used to determine when workers are eligible for transfer largely has been ignored. Some earlier studies examined the impact of this rule [5] [12] [15] but did not include labor-transfer times in their models. Gunther [6] incorporated labour-transfer times into his model, but the model involved only one worker and two machines. No previous study has examined decision rules that initiate labor transfers based on labor needs (“pull” rules). Labor transfers always have been initiated based on lack of need (“push” rules). This study examines three “pull” variations of the “When” labor-assignment decision rule. It compares their performances to the performances of two “push” rules and a comparable machine-limited system. A nonparametric statistical test, Jonckheere's S statistic, is used to test for significance of the rankings of the rules: a robust parametric multiple-comparison statistical test, Tukey's B statistic, is used to test the differences. One “pull” and one “push” decision rule provide similar performances and top the rankings consistently. Decision rules for determining when labor should be transferred from one work area to another are valuable aids for managers. This especially is true for the ever-increasing number of managers operating in organizations that recognize the benefits of a cross-trained work force. Recently there has been much interest in cross-training workers, perhaps because one of the mechanisms used in just-in-time systems to handle unbalanced work loads is to have cross-trained workers who can be shifted as demand dictates [8]. If management is to take full advantage of a cross-trained work force, it need to know when to transfer workers.     

Cognitive Limitations and Investment “Myopia”*

Optimization of investment decisions in an uncertain and dynamically evolving environment is difficult due to the limitations of the decision-maker's cognitive capacity. Thus, actual investment decisions may deviate from the dynamically optimal decision rule. This paper investigates how a potential investment rule bias affects the expected payoff from a project that has an uncertain development time and an uncertain completion cost. The result shows that the presence of a potential bias in the adopted decision rule dissipates project value and that the dissipating effect is greater for a longer term project if the completion cost is an increasing function of the time to completion.