Does "war in mixed strategies" make sense?

At yesterday's political economy workshop, our own Massimo Morelli presented a working paper that he co-authored with Matthew Jackson entitled "Strategic Militarization, Deterrence, and Wars" (paper is here). The centerpiece of the paper is an analysis of a mixed strategy equilibrium involving states playing "hawkish," "dovish", and "deterrence" strategies, with wars occurring when "hawkish" and "dovish" strategies interact.

This is the second paper that we've seen at the political economy workshop this Fall where fighting has occurred only in mixed strategies. The other paper was a working paper by Ernesto Dal Bo and Robert Powell on civil conflict resulting from a situation where governments hold private information on the size of a centrally controlled endowment from which contenders seek a share (paper is here).

This raises all the questions about whether such mixed strategy "fighting" equilibria are plausible characterizations of behavior. In the Dal Bo and Powell, paper, contenders mix over fighting and not fighting to "keep the government honest". However, the contender's decision to fight comes after she has already received her share of the endowment from the government. For the equilibrium to be believable, we have to accept that even after the contender's share has been paid out, she would still with positive probability initiate an insurgency that offers no additional gain. This strikes me as implausible.

In the Morelli and Jackson paper, things are a little better insofar as the timing of the game does not conflict so much with the logic behind the mixed strategy. But it's still a case where wars are initiated as the result of joint randomization of strategies.

However, Massimo argued for another interpretation. Rather than thinking in terms of randomizing strategies in the context of a bilateral interaction, think of one central actor facing many adversaries. Then, we can imagine a mixed strategy as being one where the central actor is playing a different strategy with each adversary such that the distribution of strategies conforms with the equilibrium "mix". My thought was that this interpretation was stretching things a bit. This interpretation would seem to require that the adversaries all act as if they are playing a bilateral game with the central actor; but clearly in any real world situation, the adversaries would condition their behavior on what the central actor is doing vis-a-vis the other adversaries. So, to be convinced, I would have see that the same equilibrium "mix" holds in a compelling, respecified game with one central actor and multiple adversaries and with the central actor choosing war with a subset of the adversaries in pure strategies. I just don't think that something like war makes any sense as an element of a mixed strategy.

Caillaud and Tirole on Group Persuasion

A paper by Caillaud and Tirole in the current AER (gated link) extends the analysis of sender-receiver games to study group persuasion. They motivate the paper with the example of the sponsor of a policy proposal attempting to persuade a committee. Here's the abstract:

The paper explores strategies that the sponsor of a proposal may employ to convince a qualified majority of members in a group to approve the proposal. Adopting a mechanism design approach to communication, it emphasizes the need to distill information selectively to key group members and to engineer persuasion cascades in which members who are brought on board sway the opinion of others. The paper shows that higher congruence among group members benefits the sponsor. The extent of congruence between the group and the sponsor, and the size and the governance of the group, are also shown to condition the sponsor’s ability to get his project approved.

And here are some of their counterintuitive results:

We showed that adding veto powers may actually help the sponsor, while an increase in external congruence [of preferences among the sponsor and committee members] may hurt him; that a [committee member with more congruent preferences to the sponsor] may be worse off than an a priori more dissonant member; and that, provided that he can control channels of communication, the sponsor may gain from creating ambiguity as to whether other members really are on board. Finally, an increase in internal congruence [of preferences among committee members] always benefits the sponsor.

On a technical note, they do not specify a game form but rather study the communication mechanisms that are optimal for the sponsor in his effort to win approval from the committee. The empirical content of the model includes some comparative statics on how size, preference congruence, and voting rules affect the likelihood of proposal acceptance and thus the stability of the policy status quo.

Non-reponse and False Response in Corruption Surveys of Firms

Abstract from a new working paper by Rahman, Li, and Jensen:

Heard melodies are sweet, but those unheard are sweeter : understanding corruption using cross-national firm-level surveys

2007-11-01

By: Rahman, Aminur; Li, Quan; Jensen, Nathan M.

http://d.repec.org/n?u=RePEc:wbk:wbrwps:4413&r=dev

Since the early 1990s, a large number of studies have been undertaken to understand the causes and consequences of corruption. Many of these studies have employed firm-level survey data from various countries. While insightful, these analyses based on firm-level surveys have largely ignored two important potential problems: nonresponse and false response by the firms. Treating firms ' responses on a sensitive issue like corruption at their face value could produce incorrect inferences and erroneous policy recommendations. We argue that the data generation of nonresponse and false response is a function of the political environment in which the firms operate. In a politically repressive environment, firms use nonresponse and false response as self-protection mechanisms. Corruption is understated as a result. We test our arguments using the World Bank enterprise survey data of more than 44,000 firms in 72 countries ! for the period 2000-2005 and find that firms in countries with less press freedom are more likely to provide nonresponse or false response on the issue of corruption. Therefore, ignoring this systematic bias in firms ' responses could result in underestimation of the severity of corruption in politically repressive countries. More important, this bias is a rich and underutilized source of information on the political constraints faced by the firms. Nonresponse and false response, like unheard melodies, could be more informative than the heard melodies in the available truthful responses in firm surveys.

This is an important type of analysis. By construction, the survey serves as an experiment to test a behavioral model of firms' willingness to report corruption. This type of "incidental survey experiment" is a nice way to perform secondary data analysis. Not only do we learn something about behavior, but we also learn something about the data itself.

Presentation on "Globalization's Losers"

In the department today, Yotam Margalit presented some results from his study on "Globalization's Losers: Trade, Culture and the Politics of Discontent." (Abstract of his research is here.) He was looking at the chain linking socio-economic attributes, negative attitudes toward globalization and integrationist policies, and then voting for right or left parties. The data that he presented suggested that predictions from the ol' Heckscher-Ohlin model do seem to conform to reality if we relate the model to income levels, assuming that owners of relatively scarce factors (conditional on economic openness) correspond to the poor in developed countries and the middle-class or rich in developing countries. But the predictions do not fare well when we relate the model to the ideological leanings of voters and parties, assuming that protectionism should be the cause of the left in developed countries and the right in developing countries. The latter prediction---specifically, that antiglobalization forces should be decidely on the left in developed countries---is not borne out by the data. Why? Margalit claims that there is a second dimension, one that he calls "perception of cultural threat," which intervenes. Antiglobalization forces, it seems, are animated by leftist economic concerns but rightist "cultural concerns." When you put the two together, you get antiglobalization voters and parties that are all over the single-dimensional ideological spectrum. When you permit parties and voters to locate themselves freely in a two-dimensional ideological space, something that proportional representation comes close to allowing, you get clustering in the "cultural right, economic left" region of the two-dimensional space.

Margalit's analysis leads us to conclude that what he labels as "cultural concerns" disrupt what otherwise would be a clean mapping between economic interests and political expression of dislike for globalization. But we are left to ponder, what exactly are these "cultural concerns"? Are they really just idiosyncratic, country-specific factors---some kind of error term---that must be studied on a case by case basis? Such was the way that Margalit responded to questions about what the cultural factors were. Does that make sense? Or are there systematic forces---racism? religion? generic fear of change?---at work here?

Applied Bargaining Models and Mechanism Design

Abstract from an interesting working paper, "Uncertainty and Incentives in Crisis Bargaining: Game-Free Analysis of International Conflict, "by Mark Fey and Kristopher Ramsay (available here):

The formal literature on international conflict has identified the combination of uncertainty and the incentive to misrepresent private information as a central cause of war. But there is a fundamental problem with using game-theoretic models to formulate general claims such as these---whether and to what extent a result that holds in a particular choice of game form continues to hold when different modeling choices are made is typically unknown. To address this concern, we present techniques from Bayesian mechanism design that allow us to establish general "game-free" results that must hold in any equilibrium of any game form in a broad class of crisis bargaining games. We focus on three different varieties of uncertainty that countries can face and establish general results about the relationship between these sources of uncertainty and the possibility of peaceful resolution of conflict. We find that in the most general setting of uncertainty about the value of war, there is no equilibrium of any possible crisis bargaining game form that allows the unilateral use of force that completely avoids the chance of costly war.

This is part of a series of papers that Fey and Ramsay have been writing on so-called "game free" analysis of crisis bargaining. The approach is appealing because it lends itself to consideration of classes of conflict resolution mechanisms that ought to be robust to changes in the bargaining procedure. As Fey and Ramsay describe, this type of analysis is especially relevant in crisis bargaining contexts. It is often the fluidity of the bargaining context that makes crisis bargaining situations distinct from institutionalized bargaining in, say, legislatures. (Although, one may argue that distributions of power may lend some structure to the bargaining situation. For example, the dynamic "ultimatum game" structure of Acemoglu and Robinson's transitions game, Boix's transitions game, and Fearon's civil war settlement game derive from an assumption about which actors have the capacity to make proposals.)

Interestingly, I came to this article after having assisted Macartan in preparing a draft of a review article on coalitional analysis. That article gives considerable attention to cooperative game theory and the Nash program. I see some similarity between what Fey and Ramsay are doing and the Nash program---basically, defining classes of games that implement axiomatic solutions.