This dissertation comprises three essays in experimental economics. The first investigates the extent of strategic behaviour in jury voting models. Existing experimental evidence in jury voting models shows subjects largely act in accordance with theoretical predictions, implying that they have the insight to condition their votes upon their own pivotality. The experiment presented here tests the extent of these abilities, finding that a large portion of subjects behave consistently with such insight in the face of several variations on the basic jury voting game, but largely fail to do so in another, perhaps due to the difficulty of extracting informational implications from counterintuitive strategies. The second investigates the extent to which hypothetical thinking - the ability to condition upon and extract information from hypothetical events - persists across different strategic environments. Two games of considerable interest in the experimental literature - jury voting games and common value auctions - each contain the feature that a sophisticated player can simplify the problem by conditioning upon a hypothetical event - pivotality and winning the auction, respectively - and extract from it information about the state of the world that might affect their own behaviour. This common element suggests that the capability that leads to sophisticated play in one should lead to the same in the other. This paper tests this connection through a within-subject experiment in which subjects each play both games. Little evidence is found that play in one relates to play in the other in any meaningful way. Finally, the third, co-authored with Evan Friedman, investigates the nature of errors relative to Nash equilibrium play in a family of two-by-two games. Using data on one- shot games, we study the mapping from the distribution of player j’s actions to the distribution of player i’s beliefs (over player j’s actions) and the mapping from player i’s payoffs (given beliefs) to the distribution over player i’s actions. In our laboratory experiment, subjects play a set of fully mixed 2 × 2 games without feedback and state their beliefs about which actions they expect their opponents to play. We find that (i) belief distributions tend to shift in the same direction as changes in opponents’ actions, (ii) beliefs are systematically biased–“conservative” for one player role and “extreme” for the other, (iii) rates of best response vary systematically across games, and (iv) systematic failures to maximize expected payoffs (given beliefs) are well explained by risk aversion. To better understand the belief formation process, we collect subject-level measures of strategic sophistication based on dominance solvable games. We find that (v) the player role itself has a strong effect on sophistication, (vi) sophistication measured in dominance solvable games strongly predicts behavior in fully mixed games, and (vii) belief elicitation significantly effects actions in a direction consistent with increasing sophistication.

This thesis is a survey of the mathematical theory of Generative Adversarial Networks (GANs). The relevant theories discussed are game theory, information theory and optimal transport theory.

將賽局理論應用於捐贈行為的文獻並不多，其中多數假設聶許臆測(Nash conjectures)且僅集中探討私人捐贈均衡條件以及其效率性問題，並未更進一步探討，政府如何運用有效的政策工具以達成福利的提升。而傳統利他(Altruism)理論多單純地以現金或實物型態的移轉支付為研究對象，認為捐贈者所關心的是受贈者的效用或消費水準。然真實生活中，常觀察到捐贈者常以現金贈與他人，受贈者雖有自由支配的權利，但捐贈者卻仍然關心受贈者如何使用此一贈款，不同的消費種類對捐贈者的效用有不同的影響（註一）。 　　本文嘗試建立一捐贈行為的賽局模型，假設受贈者消費二種不同性質的財貨勞務。首先簡單地針對一個捐贈者與一個受贈者的行為來分析，私人捐贈均衡的決定，檢視均衡是否具效率，並指出政府如何有效地運用政策工具以達成私人捐贈均衡的效率水準等三課題。此外，更進一步擴充模型放寬聶許臆測的假設，針對二個捐贈者與一個受贈者行為，同樣分析上述三項課題。 　　本文結論發現，私人捐贈均衡的決定受到捐贈者及受贈者對不同性質財貨或勞務偏好的影響。且捐贈者只有在完全搭配行為(Complete matching behavior)的臆測下，均衡才具效率。除此之外，其他臆測均衡均不具效率性。政府的介入方式若為對捐贈者進行課稅或補貼，其政策效果並不確定甚或無效；反之，政府若對受贈者的消費予以課稅或補貼，則其可明確地達成提升杜會福利的政策目標。

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 152-166).

This thesis is aimed at the optimum design of uncertain mechanical components and systems involving multiple objectives and constraints. There are various mechanical and design problems that are encountered every now and then which require the output that equalize several conflicting objectives. In recent years several methods have been developed to find a solution to multiobjective problems. The most efficient method for obtaining a compromise solution is the game theory method, which is based on the Pareto minimum or optimum solution. A thorough methodology is developed, and subsequently applied to three examples problems. The first problem is to design four helical springs which are further used to support a milling machine. The objective is to minimize the weight of the spring, also to minimize the deflection, and to maximize the natural frequency thus making the problem as a multiobjective problem. Further the subjected constraint is the shear stress constraint. After finding the optimized solution of the deterministic problem, the problem is again solved using Stochastic Nonlinear Programming, and after that it is solved using Interval Analysis. Game theory is used individually in all the three cases. The second problem is to design a gear box where the objectives are defined as the weight of the gear box, stress developed in the shaft 1, and the stress developed in shaft 2. It is subjected to nine constraints which are bending stress in teeth, contact stress of teeth, transverse displacement of shafts 1 and 2, and constraints related to the torque. The third problem is to design a power screw and the objective is to minimize the volume of the screw, and to maximize the critical buckling load and thus making it a multiobjective problem. It is subjected to constraints of being screw to be self locking, then the shear stress in screw thread, and the bearing stress in threads. The results of all the three problems that are achieved using Deterministic, Stochastic Nonlinear Programming, and Interval Analysis Method are tabulated, and the value of each objective achieved using these three methods for each problem at a time are compared to find out the most optimized solution.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 73-75). Also available in electronic version.

Research on auctions that involve more than one identical item for sale was,almost non-existing in the 90’s, but has since then been getting increasing attention. External incentives for this research have come from the US spectrum, sales, the European 3G mobile-phone auctions,  and Internet auctions. The policy relevance and the huge amount of money involved in many of them have helped the theory and experimental research advance. But in auctions where values are equal across bidders, common value auctions, that is, when the value depends on some outside parameter, equal to all bidders, the research is still embryonic. This thesis contributes to the topic with three studies. The first uses a Bayesian game to model a simple multi-unit common value auction, the task being to compare equilibrium strategies and the seller’s revenue from three auction formats; the discriminatory, the uniform and the Vickrey auction. The second study conducts an economic laboratory experiment on basis of the first study. The third study comprises an experiment on the multi-unit common value uniform auction and compares the dynamic and the static environments of this format. The most salient result in both experiments is that subjects overbid. They are victims of the winner’s curse and bid above the expected value, thus earning a negative profit. There is some learning, but most bidders continue to earn a negative profit also in later rounds. The competitive effect when participating in an auction seems to be stronger than the rationality concerns. In the first experiment, subjects in the Vickrey auction do somewhat better in small groups than subjects in the other auction types and, in the second experiment, subjects in the dynamic auction format perform much better than subjects in the static auction format; but still, they overbid. Due to this overbidding, the theoretical (but not the behavioral) prediction that the dynamic auction should render more revenue than the static fails inthe second experiment. Nonetheless, the higher revenue of the static auction comes at a cost; half of the auctions yield negative profits to the bidders, and the winner’s curse is more severely widespread in this format. Besides, only a minority of the bidders use the equilibrium bidding strategy.The bottom line is that the choice between the open and sealed-bid formats may be more important than the choice of price mechanism, especially in common value settings.

Future wireless networks will combine multiple radio technologies and subsystems, possibly managed by competing network providers. For such systems it may be advantageous to let the end nodes (terminals) make some or all of the resource management decisions. In addition to reducing complexity and costs, increasing redundancy, and facilitating more timely decisions; distributed resource sharing regimes can decouple the individual subsystems. Decoupled subsystems could be desirable both because competing operators can be business-wise separated and because it allows new technologies to be added (removed) in a modular fashion. However, distributed regimes can also lead to “selfish” wireless nodes who only try to maximize their own performance. The first part of this dissertation studies if selfish nodes can make efficient use of wireless resources, using multiaccess and network layers as examples. The related problems are formulated as noncooperative games between nodes. To maintain tractability nodes are confined to simple strategies that neither account for future payoffs nor allow for coordination. Yet, it is demonstrated that selfish nodes can achieve comparable performance to traditional protocols. These results should be interpreted as an argument in favor of distributed regimes. The second part of this dissertation evaluates the effects of multi-provider network architectures where users can roam freely across all networks. From a supply side perspective the benefits are improved path gain statistics and the fact that different networks may have non-overlapping busy hours. Several network configurations are analyzed and it is shown that cooperation between symmetric providers can yield significant capacity gains for both downlink and uplink; even if the providers have nearly collocated sites. When the providers have different site densities the gains from cooperation are reduced and the provider with a sparse network always gains more from cooperating. This suggests that initially, voluntary cooperation may be limited to some special cases. Lastly, the architecture is analyzed in a context where the providers compete for users on a per session basis by offering access at different prices. Although such architectures currently only exist in a few special cases, they could emerge in domestic markets where the costs to switch and search for new networks are low. Based on a game theoretic formulation it is shown that a competitive market for wireless access can be advantageous for both users and providers. The results presented suggest that the advantages of cooperation of competing providers occur in more than just a few cases. / QC 20100812

In this thesis we consider some network design games that arise from common network design problems. A network design game involves multiple players who control nodes in a network, each of which has a personal interest in seeing their nodes connected in some manner. To this end, the players will submit bids to a mechanism whose task will be to select which of the players to connect, how to connect their nodes, and how much to charge each player for the connection. We rely on many fundamental results from mechanism design (from [8], [9] & [5]) in this thesis and focus our efforts on designing and analyzing cost-sharing methods. That is, for a given set of players and their connection requirements, our algorithms compute a solution that satisfies all the players’ requirements and calculates ’fair’ prices to charge each of them for the connection. Our cost-sharing methods use a primal-dual framework developed by Agrawal, Klein and Ravi in [1] and generalized by Goemans &Williamson in [3]. We modify the algorithms by using the concept of death-time introduced by K¨onemann, Leonardi & Sch¨afer in [6]. Our main result is a 2-budget balanced and cross-monotonic cost sharing method for the downwards monotone set cover game, which arises naturally from any downwards monotone 0, 1-function. We have also designed a 2-budget balanced and cross-monotonic cost sharing method for two versions of the edge cover game arising from the edge cover problem. These games are special cases of the downwards monotone set cover game. By a result by Immorlica, Mahdian & Mirrokni in [4] our result is best possible for the edge cover game. We also designed a cross-monotonic cost sharing method for a network design game we call the Even Parity Connection game arising from the T-Join problem that generalizes proper cut requirement functions. We can show our algorithm returns cost shares that recover at least half the cost of the solution. We conjecture that our cost sharing method for the even parity connection game is competitive and thus 2-budget balance.

Abstract The modeling and analysis of multilateral negotiations are studied under the assumption that reaching an agreement is the main objective of the negotiators. A new methodology and associated definitions are proposed to predict the outcomes of such negotiations. The general objective of the new methodology is to study movements from one state to another in multilateral negotiations, to predict stable agreements, and to study their properties. The assumptions that the set of possible agreements is discrete and specified in advance make the negotiation problems considered here distinctive. Each decision maker has two concerns: first, achieving an alternative that is as preferable as possible; second, building support for this alternative among the other decision makers. In summary, this research consists of a systematic investigation of multilateral negotiations with the following general characteristics: • Decision makers in the negotiation seek a resolution that is not only feasible but also stable (enduring). Of course, each negotiator tries to attain the most preferable agreement for himself or herself. • If an agreement is reached, it must be an alternative from a pre-specified list, and all of the decision makers must accept the agreement. • Decision makers can possess different levels of power (or legitimacy) in support of an agreement, so the negotiation is not necessarily symmetric. Moreover, the analysis makes use of the decision makers’ preference orders over the proposed alternatives only, and does not require cardinal representations of their preferences. New concepts including State, Acceptability, Feasibility, Stability, and Fallback Distance are defined to pave the way for the proposed methodology. It is based on four types of movements, from unstable states toward stable ones, including preferential improvement, agglomeration, disloyalty move, and strategic disimprovement. Some criteria and algorithms are proposed to measure the likelihood of different moves and different outcomes. An important theorem shows that all four types of movement are mutually exclusive. The evolution of a negotiation from its status quo to the most likely outcomes is illustrated, using a tree. Several applications demonstrate that the proposed methodology can be applied to identify the most likely outcomes of a multilateral negotiation. Sensitivity analyses can be applied in several different ways to assess whether sudden or unforeseen changes in the model affect the conclusions. Several methods can be used from the literature for predicting the outcome of a negotiation. Social Choice Rules, Fallback Bargaining Procedures, and Bankruptcy Solutions are applied to the current negotiations over the legal status of the Caspian Sea to predict or recommend the most appropriate resolution among the proposed alternatives. In addition, the applicability of Graph Model for Conflict Resolution and its associated decision support system (DSS), GMCR II, are briefly discussed. Reasons why these methods are not appropriate when reaching an agreement is the main objective of decision makers (DMs) are then put forward. Based on the conceptual model for multilateral negotiations proposed in this thesis, a practical Negotiation Support System (NSS) is designed and implemented in Microsoft Access using Microsoft Visual Basic. This NSS increases the speed and accuracy of calculations. In the output of this NSS, all movements from initial states to subsequent states and their associated likelihoods are clearly illustrated, and all stable agreements are distinguished. Two real-world multilateral negotiations, over the legal status of the Caspian Sea and over the Epton site brownfield redevelopment project in Kitchener, Ontario, Canada, are modeled and analyzed using the proposed methodology. To measure DMs’ weights quantitatively in the Caspian Sea negotiations, eleven criteria that can be considered to be important determinants of countries’ capabilities are discussed, evaluated, and integrated using a Multiple Criteria Decision Analysis model. The Data Envelopment Analysis (DEA) method is employed to find the most favourable set of relative importance of different criteria for each country. Applying the proposed methodology indicates that unanimous agreements over the division of the Caspian Sea, either based on the International Law of the Seas or based on Soviet maps, are most likely as the enduring legal status of the Caspian Sea. The objective of applying the proposed methodology to actual negotiations over the redevelopment of a brownfield project is to ensure that the new methodology is flexible enough to model more real-world cases. Moreover, we wanted to test how well the actual outcomes of the real world negotiations match the most likely outcomes identified by the methodology. The results show that the decisions on the use of the Epton site followed the most likely path described and predicted by the model. This thesis is multidisciplinary in nature. It utilizes different branches of knowledge, including applied mathematics (game theory), computer science and programming, international relations, and environmental management. However, negotiation modeling and analysis in this thesis is developed from a systems engineering perspective.