The Testable Implications of Zero-sum Games

We study Nash-rationalizable joint choice behavior under restriction on zero- sum games. We show that interchangeability of choice behavior is the only additional condition which distinguishes zero-sum games from general non-cooperative games with respect to testable implications. This observation implies that in some sense interchangeability is not only a necessary but also a sufficient property which differentiates zero-sum games

Partial Identification in Two-sided Matching Models

We propose a methodology for estimating preference parameters in matching models. Our estimator applies to repeated observations of matchings among a fixed group of individuals. Our estimator is based on the stability conditions in matching models; we consider both transferable (TU) and nontransferable utility (NTU) models. In both cases, the stability conditions yield moment inequalities which can be taken to the data. The preference parameters are partially identified. We consider simple illustrative examples, and also an empirical application to aggregate marriage markets

Fragility Analysis of Space Reinforced Concrete Frame Structures with Structural Irregularity in Plan

Because significant damages to structures having structural irregularity in their plans were repeatedly observed during many past earthquakes, there have been great research efforts to evaluate their seismic vulnerability. Although most of the previous studies used simplified structural representations such as one-dimensional or two-dimensional models in the fragility analysis of plan-irregular structures, simple analytical models could not represent true seismic behavior from the complicated nonlinear coupling between lateral and torsional responses as the degree of irregularity increased. For space structures with high irregularity, more realistic representations such as three-dimensional models are needed for proper seismic assessment. However, the use of computationally expensive models is not practically feasible with existing approaches of fragility analysis. Thus, in this study, a different approach is adopted that can produce vulnerability curves efficiently, even with a three-dimensional model. In this approach, an integrated computational framework is established that combines reliability analysis and structural analysis. This enables evaluation of the limit-state faction without constructing its explicit formula, and the failure probability is calculated with the first-order reliability method (FORM) to deal with the computational challenge. Under the integrated framework, this study investigates the seismic vulnerability of space reinforced concrete frame structures with varying plan irregularity. Material uncertainty is considered, and more representative seismic fragility curves are derived with their three-dimensional analytical models. The effectiveness of the adopted approach is discussed, and the significant effect of structural irregularity on seismic vulnerability is highlighted

Single-Crossing Differences in Convex Environments

An agent's preferences depend on an ordered parameter or type. We characterize the set of utility functions with single-crossing differences (SCD) in convex environments. These include preferences over lotteries, both in expected utility and rank-dependent utility frameworks, and preferences over bundles of goods and over consumption streams. Our notion of SCD does not presume an order on the choice space. This unordered SCD is necessary and sufficient for ''interval choice'' comparative statics. We present applications to cheap talk, observational learning, and collective choice, showing how convex environments arise in these problems and how SCD/interval choice are useful. Methodologically, our main characterization stems from a result on linear aggregations of single-crossing functions

Strategic Voting in a Jury Trial with Plea Bargaining

Abstract We study a model of the criminal court process focusing on the interaction between plea bargaining and a jury trial. A prosecutor and a defendant participate in plea bargaining while anticipating possible outcomes of the jury trial. We assume that plea bargaining produces a bias in which the jury believes the defendant is less likely to be guilty if the case goes to trial. Consequently, the bias alters the trial outcome which is assumed to follow a strategic voting model. We find that the equilibrium behavior in the court process with plea bargaining and a jury trial resembles the equilibrium behavior in the separate jury model. However, unlike in the case of jury model, the jurors may act as if they have the prosecutor's preference against convicting the innocent and acquitting the guilty. Overview Introduction The U.S. criminal court system has numerous steps which allow attorneys and defendants to actively participate throughout the process. Although the details differ from state to state, in general the criminal court process consists of an arrest, preliminary hearings, plea negotiations, a jury trial, and a verdict. Most people think that all sentences are delivered by a jury trial, but a significant number of cases are resolved in a pre-trial stage. Plea bargaining is one such case where a defendant is allowed to plead guilty in exchange for a lenient charge. Plea bargaining is so prevalent that, among 88,094 defendants during 2006, 76,778 (or 87%) were terminated by pleading guilty or no-contest. 1 The fact that litigation ends in the plea bargain stage in 1 Bureau of Justice Statistics in Office of Justice Programs, U.S. Department of Justice. http://www.ojp.usdoj.gov/bjs 1 the vast majority of cases causes people to believe that a trial is not important. However, this conclusion is inaccurate since the trial directly follows when the participants in the plea bargain fail to reach an agreement. In fact, research in legal studies suggests that plea bargaining and a jury trial closely interact with each other, and this interaction plays a significant role in the entire court process. Although most cases are settled before the jury trial, participants in the plea bargain anticipate possible outcomes of the jury trial if they fail to reach an agreement. In this sense, a primary role of a jury trial may be allocating bargain power to each side of plea bargain participants rather than handling cases directly. 2 On the other hand, the jury trial hinges on the consequences of the plea bargain. The incentive to plead guilty differs if the defendant is truly guilty or innocent, so cases with innocent defendants tend to go to the trial. The jury trial incorporate this selection bias in its verdict. 3 In this paper, we study a model of a criminal court process focusing on the interaction between plea bargaining and a jury trial. While the previous literature studies either plea bargaining assuming an exogenously given trial behavior, or a jury trial assuming an exogenous litigation process, our model allows the plea bargain and the jury trial to interact with each other in a unified model. A prosecutor and a defendant participate in plea bargaining while anticipating possible outcomes of the jury trial, and the jurors incorporate that the defendant whom they face denied the crime and pleaded not guilty. The pleading decision and the jury trial behavior resembles a signaling game. Given a plea bargain punishment, a defendant, as a sender, signals his type by pleading either guilty or not guilty. Then the jury, as a receiver, updates the belief on the sender's type and determines conviction probabilities. Consider for example that the jurors believe a certain proportion of the defendants in the jury trial are guilty. During the trial, each juror obtains additional information on the defendant and decides whether to vote for conviction or acquittal. Intuitively, a guilty defendant will have a higher chance to be convicted than an innocent defendant. The conviction probabilities (one for guilty and the other for innocent defendants) become higher as jurors believe that more guilty defendants come to trials. Given a plea bargain offer by the prosecutor, a defendant compares the offer and the outcome 2 Mnookin and Kornhauser (1979) represent this observation as "Bargaining in the shadow of the law". 3 The strategic voting model captures this as a belief on the prior probability of a guilty defendant which in turn affects the conviction probability. 2 of the jury trial. Basically, a defendant pleads guilty if the bargain offers less punishment than the expected punishment from the jury trial. However, since this pleading decision affects the jurors' belief on the proportion of guilty defendants, it is not clear what will be the final outcome. Our intuition is as follows. (1) If the bargain offer for guilty defendants is acceptable compared to the jury trial behavior, all guilty defendants plead guilty. Then the jurors update their belief on the proportion of the guilty defendants in the trial and lower conviction probabilities. Then the bargain offer becomes unacceptable. (2) If the bargain offer is unacceptable, the opposite story follows. As the jurors assumes that more guilty defendants come to trial, the jurors tend to increase the conviction probabilities. Then the bargain offer may become acceptable. In general, the consequences of the punishment from pleading guilty and of the expected punishment from the trial would become equivalent for 'guilty' defendants. Since innocent defendants have less chance to be convicted in the trial, they will not plead guilty. Therefore, the ex-ante punishment levels for guilty and innocent defendants are the same as the conviction probabilities in the jury trial. The prosecutor's objective is to deliver punishment to guilty defendants while minimizing mistakes of punishing innocent defendants. To achieve the objective, the prosecutor controls the level of the plea bargain offer. Observations in the previous paragraph imply that the prosecutor may want to manipulate the jury trial behavior so that it renders the expected levels of punishment ideal. We later show that such manipulation leads each juror to vote as if she has the prosecutor's preference against convicting the innocent and acquitting the guilty. However, such manipulation is possible only if the prosecutor cares more than jurors about the mistakenly delivered punishment to innocent defendants. Our study generalizes the strategic voting model beyond the jury trial to the criminal court process. In strategic voting literature, it is a convention to assume that litigation is exogenously given. However, defendants and prosecutors actively participate in pre-trial stages, so implications of the strategic voting model may not be directly applicable to the entire court process. By attaching a model on plea bargaining to the strategic voting model, we show that the model can be nicely extended to cover the complete court process. As an example, we compare two voting paradigms, the unanimity and non-unanimous rules. Feddersen and Pesendorfer (1998) compare these paradigms in a jury trial context and conclude that the unanimity rule is inferior. The probabilities of convicting the innocent and acquitting the guilty do not vanish as the number of jurors get large, whereas these probabilities vanish 3 to zero under any non-unanimous rule. We show that this conclusion is preserved under plea bargaining. This paper also sheds light on an economic justification of plea bargain, which is not motivated by saving trial costs. 4 We assume that a trial is free. Not only are explicit costs such as time and efforts excluded, but all players are also assumed to be risk neutral; they are unafraid of uncertain jury trial outcomes. Plea bargaining allows the court to screen out some guilty defendants before going to a jury trial. The accused know whether they are guilty, and plea bargaining serves as a self-selection mechanism. By doing so, it may contribute to the accuracy of the jury trial which the entire court performance hinges on. Related Literature Our paper shares motivations in several other papers exploring strategic behavior in a criminal court process. Related literature can be divided into those studying jury trials and those studying plea bargaining. It is undeniable that plea bargaining originated as a way of avoiding jury trial costs at the beginning. However, its welfare effects on other than trial costs have received less attention. Jury Trial Grossman and Priest and Klein (1984) study litigation rather than plea bargaining, but it is one of the closest studies to our paper. Priest and Klein model a litigation process that clarifies the relationship between the set of disputes settled and the set litigated. An important assumption is that the potential litigants produce rational estimates of the likely decision by possibly biasing the belief of the jury. The paper shows the disputes selected for litigation are determined endogenously, and they may differ from a representative sample of the set of all disputes. The motivation coincides with of our paper in the sense that jury trial models disregarding endogenous settlement may give inaccurate implications. While Priest and Klein informally model how the biased jury belief affects the jury decision, we construct a jury decision process through exploiting the strategic voting model. The Model A criminal court process begins with a prosecutor indicting a suspect. We assume that the defendant is either guilty (G) or innocent (I), which occur with equal probabilities. The prosecutor suggests a take-it-or-leave-it plea bargain offer with θ ∈ [0, 1] proportion of the original charge. The defendant can plead either guilty or not guilty. If the defendant pleads guilty, the case terminates and the punishment θ is delivered. Otherwise, the plea bargain is withdrawn, and the case goes to a jury trial. A plea bargain gives the defendant an opportunity to avoid the judgment of conviction on the original charge. 5 We refer prosecutors and defendants male, and jurors female. Our jury model is based on a strategic voting hypothesis in where p ∈ (.5, 1); a juror receives a correct signal with probability p and the incorrect signal with probability 1 − p. The jury reaches a decision by casting votes simultaneously. Each juror can vote for either conviction or acquittal. If the number of conviction votes is larger than the voting rulek, the defendant is convicted (C). Otherwise, the defendant is acquitted (A). The punishment accompanied by C and A are normalized by 1 and 0 respectively. Consequently, the punishment by pleading guilty becomes θ. Our model assumes that all players behave rationally where each acts to maximize an appropriately defined utility function. The defendant's utility changes negatively by the amount of punishment; −1 if he is convicted, 0 if he is acquitted, and −θ if he pleads guilty. He is assumed to be risk neutral; if he perceive that he will be convicted with probability s, then the ex ante utility of going to trial is s · 1 + (1 − s) · 0. The defendant wants to minimize the punishment and thus maximize his expected utility. All jurors have an identical preferences. We normalize the utility functions so that correct 67 Finally, we assume that the prosecutor has a preference defined on [0, 1] × {G, I}. Much like the jurors', when the punishment h ∈ [0, 1] is delivered to a defendant, the prosecutor's utility 6 Suppose a juror believes that the defendant is guilty with probabilityq. The expected utility of a guilty verdict (−q(1 −q)) is greater than or equal to the expected utility of an innocent verdict (−(1 − q)q) if and only ifq ≥ q. Therefore when jurors vote for conviction, they use q as the threshold level of belief that the defendant is guilty. In this respect, Feddersen and Pesendorfer (1998) term q "the threshold level of reasonable doubt." 7 q < 0.5 requires additional technical conditions, but the analysis is qualitatively intact. 7 is given by The prosecutor is assumed to act in a state's or a social planner's interest. Critics may argue that we should alternatively consider a self-interested prosecutor who would maximize for example the total sum of delivering punishment or the average conviction probability in trial. However in actual situations, because a mistakenly managed case may becomes public later, such case will affect a prosecutor's future career. A self-interested prosecutor will be concerned with false prosecutions. We represent this concern with flawed cases with a parameterized weight, q ′ . Jury Trial Let π denote the updated prior probability that a defendant is guilty conditioned that the case comes to a trial. We assume that a jury trial has less chance to meet a guilty defendant than an innocent defendant (π ≤ .5). This assumption is not lose generality. First, it is natural that each juror is more likely to vote for a conviction when she receives a guilty signal g, rather than i. (We formally show this soon.) Since guilty defendants are more likely send signal g, guilty defendants have more chance to be convicted. As defendants anticipate such jury trial outcomes, guilty defendants tend to plead guilty and are less likely to litigate compared to innocent defendants. A map σ j : {g, i} → [0, 1] represents a strategy of juror j. The juror votes for conviction with 8 A government cannot perfectly observe prosecutor's effort to avoid false prosecutions, and this yields a principleagent problem. Although in general even well-designed incentives cannot lead the prosecutor's actions and the government's interests to perfectly coincide, we do not consider the agent problem in this paper. probability σ j (g) when she receives a signal g; whereas, she votes for conviction with probability σ j (i) if the signal is i. In this paper, we consider symmetric equilibria in which all jurors adopt the same strategy. We denote a symmetric strategy profile as [σ(g), σ(i)] without specifying a particular juror. Since the jury trial is modeled as a symmetric game, there exists at least one symmetric Nash equilibrium. We then find a symmetric equilibrium which gives all jurors the highest expected coordinated payoff. Since all jurors have the same preference for judicial decisions, especially convicting innocent and acquitting guilty people, this is a natural way of refining equilibria. We call this refined equilibrium an Efficient symmetric Nash equilibrium, or more succinctly an Efficient equilibrium. A single juror affects the verdict only when she is in the pivotal position. 9 Assuming that the juror acts rationally, she takes into account that not only the private signal (g or i), but also the additional information from the event that she is pivotal (piv) as the evidence of guilty. The juror also knows that some defendants plead guilty, so the guilty to innocent ratio of defendants in jury trial is and The left hand side (LHS) is the likelihood ratio of guilty to innocent, given that a juror is pivotal, multiplied by the likelihood ratio of private information (g or i), times the ratio of updated prior probabilities; and the right hand side (RHS) is the ratio of reasonable doubt. If the LHS is larger than the RHS in equation To state the pivotal probabilities precisely, let us denote r G as the probability of voting for conviction when the defendant is guilty, and r I for the same probability when the defendant is innocent. Since a guilty defendant and an innocent defendant send signal g with probability p 9 Whether a juror is pivotal or not, of course, depends not only on how the other jurors vote but also on the voting rule -unanimity, simple majority, and three-fourths, etc. 10 and 1 − p respectively, we obtain When a voting rule requiresk (1 ≤k ≤ n) number of conviction votes for a guilty verdict, a juror becomes pivotal whenk −1 other jurors vote for conviction. Assuming that 0 < r G , r I < 1, the voting criterion (2) becomes and the criterion (3) becomes When r G = r I = 0 or r G = r I = 1, The above equations are necessary conditions for a jury trial equilibrium, and we use the necessary conditions to characterize equilibrium strategy profiles. An additional definition simplifies the equilibrium expression. Let us define a functionπ from N to [0, q] as π(l ; p, q) := 1 which is strictly decreasing in l. We can rearrange the expression and obtain The functionπ maps a number of guilty signals (l) to the level of updated prior probability (π) which barely gives an enough incentive for a conviction vote. That is,π(l) is the minimum level of prior such that l number of guilty signals lead a juror to vote for conviction. Although equilibria have complicated expressions, the motivation behind is straightforward. Suppose an updated prior π is less thanπ We relegate details of equilibrium computation to Appendix A, and only state equilibrium properties in Lemma 1. If the conviction probability with the signal g is strictly higher than the probability with the signal i, we say the equilibrium is responsive. Lemma 1 shows that a responsive equilibrium, if exists, is more efficient than a non-responsive. Proposition 1 Jury Trial Behavior For a given π, (σ(g; π), σ(i; π)) denotes the set of efficient equilibrium strategy pairs. denotes the set of corresponding conviction probability pairs of a guilty and an innocent defendant, respectively. Plea Bargaining Distribute let φ G and (1 − φ G ) denote the probability of a guilty defendant pleads guilty and not guilty, respectively. φ I and (1 − φ I ) are defined similarly for an innocent defendant. Let π be the updated prior probability of guilty defendant conditioned that a case comes to a trial. Provided that not all cases terminate in plea bargaining (φ G > 0 or φ I > 0), π is determined as 13 If all defendants plead guilty (φ G = φ I = 1), the updated prior is assumed to be equal to 0. optimal bargain offer θ * , which yields the highest equilibrium payoff. The jury trial delivers punishment equal to either 0 (acquittal) or 1 (conviction), whereas a plea bargain can deliver any punishment, h ∈ [0, 1]. Delivering punishment to a guilty defendant and dismissing punishment with an innocent defendant give zero utility; dismissing punishment with a guilty defendant changes utility by −(1 − q ′ ), and delivering punishment to an innocent defendant changes utility by −q ′ . Although the prosecutor's utility has a similar format to the jurors', we do not interpret q ′ as a level of reasonable doubt; we treat it as relative weights on incorrect decisions. Suppose a prosecutor offers a defendant an opportunity to plead guilty with charge θ ∈ [0, 1]. Given conviction probabilities (P G , P I ), the defendant compares θ with either P G or P I , and decides whether to plead guilty or to go to trail. If θ is larger than P G , no guilty defendant has an incentive to plead guilty (φ G = 0); similarly, if θ is larger than P I , no innocent defendant pleads guilty. The updated prior probability, π = 1−φG (1−φG)+(1−φI ) , reflects pleading decisions. 11 Conversely, jurors incorporate the updated prior in their voting behavior, thus conviction probabilities, (P G , P I ) ∈ (P [C|G, π], P [C|I, π]) are changed by π, which become 10 Although we can derive this assumption by applying an equilibrium refinement, D1 11 Note that we also assumed π = 0 in case of φG = φI = 1. 14 basis of pleading decision. Given θ, the subgame equilibrium is determined as a fixed point in this pair of two dynamics. The prosecutor wants to set θ which yields the highest subgame equilibrium payoff. We summarize the prosecutor's problem as an optimization under constraints. such that otherwise. The first term in the object function is the utility changed by mistakenly delivered punishment to the innocent with plea bargaining and the jury trial, respectively. The second term is the utility changed by mistakenly undelivered punishment to the guilty. Condition (a.1) and (a.2) represent pleading decisions by a guilty and an innocent defendant, respectively. Condition (b) requires the pair of conviction probabilities to be consistent with equilibrium outcome under π, and (c) captures how the prior is updated. The prosecutor wants to maximize the equilibrium payoff with adjusting θ. Lemma 2 allows us to simplify the above problem. Given a θ, suppose we have θ < P [C|G, π] in an equilibrium. It is necessary that a guilty dependent must plead guilty, and the jury faces no guilty defendant: π = 0. However, P [C|G; π = 0] = 0 implies that θ < P [C|G, π] must not be true. Whereas if θ > P [C|G, π], no defendant pleads guilty, and the updated prior must be equal to the initial prior (π = .5). Therefore, θ ∈ P [C|G; π] is a necessary condition when the equilibrium π is in [0, .5). The following lemma formally states this observation which we will use to simplify the prosecutor's problem. Lemma 2 Suppose the prosecutor offers θ for pleading guilty. Given that the jury choose an efficient equilibrium, one of the followings and only one must be true. 12 12 In this paper, we assume that the updated prior probability π is equal to 0 when all defendants plead guilty. Indeed, Perfect Baysian Equilibrium allows any level of π ∈ [0, 1] as the belief off-the equilibrium path φG = φI = 1. The condition D1 in 15 • θ > P G and φ G = φ I = 0 and π = .5. • θ = P G with P G ∈ P [C|G, π] with (φ G , φ I ) obtaining such π. Proof : Clearly, if θ > P G , and necessarily θ > P I , then no defendant pleads guilty. φ G = φ I =

Institutions, fiscal transparency and fiscal policy outcomes

We examine how institutions influence the government’s decisions on reporting and revising its fiscal data, and reforming its accounting system into an accrual basis. The effect of accrual accounting adoption on fiscal policy outcomes is also studied. While the literature analyzes only developed countries, we construct the extensive panel data including less developed countries and show that institutions play a different role in fiscal policy decisions and outcomes between the developed and the less developed ones. In Chapter 1, we investigate how the government reports and revises its fiscal data. We find that while rule of law, legislative electoral competition, financial openness and population enhance reporting the fiscal data, natural resource rents, executive electoral competition and cabinet size prevent it. Also, we suggest that GDP per capita, bureaucratic quality, a presidential regime, election in the next year and ethno-linguistic fractionalization make the government diminish the time lag of reporting. Recently, trends that the government opens a small deficit at first and revises it to a big deficit later have been found. We show that these revisions come from a bias of initially released fiscal data as well as new information after the initial release. Also, while the early-reporting government releases balance initially without a bias in the developed countries, the late-reporting government does in the less developed ones. Lastly, we discover that fiscal rules, administrative quality and inflation diminish revisions from a small to a big deficit, but responsiveness of the government to people expands them in the developed countries. However, only real GDP growth decreases them significantly in the less developed countries. In Chapter 2, we study which factors determine accrual accounting adoption among governments. We find that wealth such as GDP per capita and democracy facilitate the adoption consistently in all countries. However, while political competition, common law tradition, spread of accrual accounting among other governments and rule of law enhance the adoption in the developed countries, bureaucratic quality, education and economic stability are the important factors to encourage it in the less developed countries. In Chapter 3, we look into how the adoption of accrual accounting affects fiscal policy outcomes such as debt, balance and the discrepancy between a net increase of debt and a deficit that is a proxy for fiscal transparency. We discover that while the adoption diminishes debt in the developed countries, it expands them in the less developed ones. These effects become strong in highly-indebted countries. The adoption improves balance in the developed countries and worsens it in the less developed ones, which is significant only in the developed ones with big deficits. Also, it lessens the discrepancy significantly and improves fiscal transparency only in the less transparent developed countries

Incentive Compatibility of Large Centralized Matching Markets

This paper discusses the strategic manipulation of stable matching mechanisms. We provide a model of a two-sided matching market, in which a firm hires a worker, and each of them receives non-transferable utility. Assuming that the utilities are randomly drawn from underlying distributions, we measure the likelihood of differences in utilities from different stable matchings. Our key finding is that in large markets, most agents are close to being indifferent among partners in different stable matchings. Specifically, as the number of firms and workers becomes large, the expected proportion of firms and workers whose utilities from all stable matchings are within an arbitrarily small difference of one another converges to one. It is known that the utility gain by manipulating a stable matching mechanism is limited by the difference between utilities from the most and the least preferred stable matchings. Thus, the finding also implies that the expected proportion of agents who may obtain a significant utility gain from manipulation vanishes in large markets. This result reconciles successful stable mechanisms in practice with the theoretical concerns about strategic manipulation