The Impact of Conventional Force Reductions on Strategic Deterrence: A Game-Theoretic Analysis

Many game-theoretic analyses of deterrence confirm the commonsense view that what determines whether a defender can effectively deter a challenger from an unwanted action is (1) the challenger’s perception of the level of punishment that the defender will be able to impose on the challenger should it take the action, and (2) the challenger’s level of belief about the likelihood of the defender actually carrying out this punishment. Reduction of the defender’s forces may affect both the defender’s ability to retaliate and its perceived willingness to do so. Game-theoretic methods are used to assess how the limits on both of these parameters are related, subject to the condition that deterrence remains effective. The results indicate that the defending side can often make do with smaller forces, provided its (apparent) resolve is high. But force structure is important—the models suggest that implementation of an “all-or-nothing” deployment (as called for by a doctrine of massive retaliation, for example) may reduce not only costs, but also deterrence effectiveness

Are stable agreements for sharing international river waters now possible?

International river and lake basins constitute about 47 percent of the world's continental land area, a proportion that increases to about 60 percent in Africa, Asia, and South America. Because water is a scarce and increasingly valuable resource, disputes about water allocation within these basins often contribute to regional tensions and conflicts. May principles of international law have been developed to allocate water within a water basin and to prevent or resolve international water disputes. Unfortunately, they rarely are easy to apply and often are contradictory. Sharing river water is particularly difficult because the effects are one-way, with upstream-downstream supply disputes have been among the most common. Agreements about the allocation of river water often last only until the first drought, when reduced flow denies some their full shares. The authors develop a simple formal model of water allocation among states within a river basin. They analyze the model in the context of variable flow rates, to project the behavior of riparian states during periods of above-normal and below-normal flow. Their objective: to understand when, where, and how much the economic interests of the states conflict, to develop principles guaranteeing efficient allocations of scarce water supplies, and to identify when stable (self-enforcing) allocation agreements are possible. They also consider the possibility of using alternative sources of supply and of accommodating growth in demand. Satellite technology will soon dramatically improve the ability of riparian states to predict annual flow volumes. In addition, water basin authorities will have real-time data on riparians'water use. These developments will have important implications for the enforceability and the flexibility of river water allocation systems. This model shows how flexibility can be used to construct more durable systems for sharing water among riparian states. The new allocation methods proposed here should contribute to the better management of scarce water supplies, a crucial issue in an increasingly thirsty world.Water and Industry,Water Conservation,Environmental Economics&Policies,Water Supply and Systems,Decentralization,Water Supply and Sanitation Governance and Institutions,Town Water Supply and Sanitation,Water Conservation,Water and Industry,Environmental Economics&Policies

Kingmakers and leaders in coalition formation

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they “fall back” on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the players common to them, or kingmakers, determine which fallback coalition will form. The first player(s) acceptable to all other members of a fallback coalition are the leader(s) of that coalition. The effects of different preference assumption--particularly, different kinds of single-peakedness--and of player weights on the number of coherent coalitions, their connectedness, and which players become kingmakers and leaders are investigated. The fallback procedure may be used (i) empirically to identify kingmakers and leaders or (ii) normatively to select them. We illustrate and test the model by applying it to coalition formation on the U.S. Supreme Court, 2005-2009, which shows the build-up over stages of a conservative coalition that prevailed in nearly half of the 5-4 decisions.coalition formation; fallback procedure; kingmakers; leaders; US Supreme Court

Games That End in a Bang or a Whimper

Using truels, or three-person duels, as an example, we show that how players perceive a multiple-round game will end can make a big difference in whether it ends non-cooperatively (producing a "bang") or just peters out (producing a "whimper"): 1. If the players view the number of rounds as bounded-reasonable, because the game must end in a finite number of rounds-they will shoot from the start. 2. If the players view the number of rounds as unbounded-reasonable, because the horizon of the game is infinite-then a cooperative equilibrium, involving no shooting, can also occur. Real- life examples are given of players with bounded and unbounded outlooks in truel- like situations. Unbounded outlooks encourage cooperative play, foster hope, and lead to more auspicious outcomes. These outcomes are facilitated by institutions that put no bounds on play-including reprisals-thereby allowing for a day of reckoning for those who violate established norms. Eschatological implications of the analysis, especially for thinking about the future and how it might end, are also discussed.TRUELS; BACKWARD INDUCTION; INFINITE-HORIZON GAMES; ESCHATOLOGY

Water Supply Planning under Interdependence of Actions: Theory and Application

An ongoing water supply planning problem in the Regional Municipality of Waterloo, Ontario, Canada, is studied to select the best water supply combination, within a multiple-objective framework, when actions are interdependent. The interdependencies in the problem are described and shown to be essential features. The problem is formulated as a multiple-criteria integer program with interdependent actions. Because of the large number of potential actions and the nonconvexity of the decision space, it is quite difficult to find nondominated subsets of actions. Instead, a modified goal programming technique is suggested to identify promising subsets. The appropriateness of this technique is explained, and the lessons learned in applying it to the Waterloo water supply planning problem are described

Stabilizing Power Sharing

Power sharing is modeled as a duel over some prize. Each of two players may either share the prize in some ratio or fire at the other player—either in sequence or simultaneously—and eliminate it with a specified probability. If one player eliminates the other without being eliminated itself, it captures the entire prize, but the prize is damaged over time when there is shooting. Simultaneous shooting, which is more damaging than sequential shooting, tends to induce the players to share the prize and expand their opportunities for sharing it. It was effectively implemented by the superpowers with the doctrine of “launch on warning” during the Cold War, and it was strengthened by the development of second-strike capability. Deterring terrorism has proved a different matter, because terrorists are difficult to detect and present few targets that can be damaged.power sharing, game, duel, deterrence, terrorism

The Instability of Power Sharing

Three models are presented in which two players agree to share power in a particular ratio, but either player may subsequently “fire” at the other, as in a duel, to try to eliminate it. The players have positive probabilities of eliminating each other by firing. If neither is successful, the agreement stays in place; if one is successful, that player obtains all the power; if each eliminates the other, both players get nothing. In Model I, the game is played once, and in Model II it is repeated, with discounting of future payoffs. Although there are conditions under which each player would prefer not to shoot, satisfying these conditions for one player precludes satisfying them for the other, so at least one player will always have an incentive to shoot. In anticipation, its rival would prefer to shoot, too, so there will be a race to preempt. In Model III, a damage factor caused by shooting, whether successful or not, is introduced into Model II. This mitigates the incentive to shoot but does not eliminate it entirely. The application of the models to conflicts, especially civil wars, is discussed.power sharing, repeated game, duel, civil wars

How democracy resolves conflict in difficult games

Democracy resolves conflicts in difficult games like Prisoners’ Dilemma and Chicken by stabilizing their cooperative outcomes. It does so by transforming these games into games in which voters are presented with a choice between a cooperative outcome and a Pareto-inferior noncooperative outcome. In the transformed game, it is always rational for voters to vote for the cooperative outcome, because cooperation is a weakly dominant strategy independent of the decision rule and the number of voters who choose it. Such games are illustrated by 2-person and n-person public-goods games, in which it is optimal to be a free rider, and a biblical story from the book of Exodus.Democracy; voting; social choice; public goods; game theory; Prisoners' Dilemma; Bible

When does approval voting make the "right choices"?

We assume that a voter’s judgment about a proposal depends on (i) the proposal’s probability of being right (or good or just) and (ii) the voter’s probability of making a correct judgment about its rightness (or wrongness). Initially, the state of a proposal (right or wrong), and the correctness of a voter’s judgment about it, are assumed to be independent. If the average probability that voters are correct in their judgments is greater than ½, then the proposal with the greatest probability of being right will, in expectation, receive the greatest number of approval votes. This result holds, as well, when the voters’ probabilities of being correct depend on the state of the proposal; when the average probability that voters judge a proposal correctly is functionally related to the probability that it is right, provided that the function satisfies certain conditions; and when all voters follow a leader with an above-average probability of correctly judging proposals. However, it is possible that voters may more frequently select the proposal with the greatest probability of being right by reporting their independent judgments—as assumed by the Condorcet Jury Theorem—rather than by following any leader. Applications of these results to different kinds of voting situations are discussed.Approval voting; election systems; referendums; Condorcet jury theorem

Narrowing the field in elections: the next-two rule

We suggest a new approach to narrowing the field in elections, based on the deservingness of candidates to be contenders in a runoff, or to be declared one of several winners. Instead of specifying some minimum percentage (e.g., 50) that the leading candidate must surpass to avoid a runoff (usually between the top two candidates), we propose that the number of contenders depend on the distribution of votes among candidates. Divisor methods of apportionment proposed by Jefferson and Webster, among others, provide measures of deservingness, but they can prescribe a runoff even when one candidate receives more than 50 percent of the vote. We propose a new measure of deservingness, called the Next-Two rule, which compares the performance of candidates to the two that immediately follow them. It never prescribes a runoff when one candidate receives more than 50 percent of the vote. More generally, it identifies as contenders candidates who are bunched together near the top and, unlike the Jefferson and Webster methods, never declares that all candidates are contenders. We apply the Next-Two rule to several empirical examples, including one (elections to major league baseball’s Hall of Fame) in which more than one candidate can be elected.voting; contenders in elections; runoffs; apportionment; fairness