Essays in organization formation and decision making

This thesis consists of three essays in microeconomic theory. The first two are about the formation of organizations, and the third is about individual or organizational decision making in ambiguous settings. In the first essay I explore the implications of costs associated with binding agreements on equilibrium agreement structures. Establishing binding agreements is often costly in real world economies. These contracting costs are usually regarded as harmful by economists as the costs decrease the gains from cooperation. They affect which agreements form by changing the incentives of agents, potentially prevent the establishment of efficient contracts. Using an alternating offers bargaining model of coalition formation I show that the presence of transaction costs can lead to an efficient outcome in situations where inefficiency arises in equilibrium without these costs. These results provide new insights for policies targeting transaction costs. There are many situations in Economics and Political Science that involve limited possibilities for firms or parties to organize themselves into groups, mostly due to regulatory restrictions. In addition, in these settings the surplus of a given group often depends on the organizational structures formed outside of the group. The second essay introduces a coalition formation model that is able to analyze markets with both restricted cooperation and externalities across coalitions. This concept allows a more realistic modeling, opening the possibility to use this framework to analyze the welfare effects of mergers. In the third essay I propose a new model of decision making under uncertainty with multiple priors that is, unlike the well-known model of Gilboa and Schmeidler (1989), able to express attitude towards ambiguity. In addition, the decision does not necessarily depend on the two extreme (worst case and best case) priors as in the model of Ghirardato et al. (2001). I use choice correspondences by lexicographic semiorders that are generalizations of the choice functions defined in Manzini and Mariotti (2012). I also provide a method constructing lexicographic semiorders for choosing from ambiguous acts

Bargaining and the theory of cooperative games: John Nash and beyond

This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162).Nash's bargaining model, Nash solution, Kalai-Smorodinsky solution, Egalitarian solution

Copmment on Egalitarianism under Incomplete Information

The paper aims at extending the egalitarian principle to environments with incomplete information. The approach is primarily axiomatic, focusing on the characteristic property of monotonicity: no member of the society should be worse off when more collective decisions are available. I start by showing the incompat- ibility of this property with incentive efficiency, even in quasi-linear environments. This serious impossibility result does not follow from the mere presence of incentive constraints, but instead from the fact that information is incomplete (asymmetric information at the time of making a decision). I then weaken the monotonicity property so as to require it only when starting from incentive compatible mecha- nisms at which interim utilities are transferable (in a weak sense). Adding other axioms in the spirit of Kalai's (Econometrica, 1977, Theorem 1) classical character- ization of the egalitarian principle under complete information, I obtain a partial characterization of a natural extension of the lex-min solution to problems with incomplete information. Next, I prove that, in each social choice problem, there is a unique way of rescaling the participants' interim utilities so as to make this solu- tion compatible with the ex-ante utilitarian principle. These two criteria coincides in the rescaled utilities exactly at the incentive ecient mechanisms that maxi- mize Harsanyi and Selten's (Management Science, 1972) weighted Nash product. These concepts are illustrated on classical examples of profit-sharing, public good production and bilateral trade. The richness of the topic of social choice under in- complete information is illustrated by considering two alternative extensions of the egalitarian principle { one based on an idea of equity from the point of view of the individuals themselves (given their private information) instead of an uninformed third party (social planner or arbitrator), and another notion based on the idea of

On the existence of strategic solutions for games with security- and potential level players

This paper examines the existence of strategic solutions for finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Gilboa, 1988; Jaffray, 1988; Cohen, 1992). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, 1950a,b) or for equilibria in beliefs (Crawford, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, 1984; Moulin, 1984; Pearce, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players

Fair integer programming under dichotomous preferences

One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables represent agents with dichotomous preferences, who only care about whether they are selected in the final solution. We develop several general-purpose algorithms to fairly select optimal solutions, for example, by maximizing the Nash product or the minimum selection probability, or by using a random ordering of the agents as a selection criterion (Random Serial Dictatorship). As such, we embed the black-box procedure of solving an integer linear program into a framework that is explainable from start to finish. Moreover, we study the axiomatic properties of the proposed methods by embedding our framework into the rich literature of cooperative bargaining and probabilistic social choice. Lastly, we evaluate the proposed methods on a specific application, namely kidney exchange. We find that while the methods maximizing the Nash product or the minimum selection probability outperform the other methods on the evaluated welfare criteria, methods such as Random Serial Dictatorship perform reasonably well in computation times that are similar to those of finding a single optimal solution

Algorithmic and complexity aspects of simple coalitional games

Simple coalitional games are a fundamental class of cooperative games and voting games which are used to model coalition formation, resource allocation and decision making in computer science, artificial intelligence and multiagent systems. Although simple coalitional games are well studied in the domain of game theory and social choice, their algorithmic and computational complexity aspects have received less attention till recently. The computational aspects of simple coalitional games are of increased importance as these games are used by computer scientists to model distributed settings. This thesis fits in the wider setting of the interplay between economics and computer science which has led to the development of algorithmic game theory and computational social choice. A unified view of the computational aspects of simple coalitional games is presented here for the first time. Certain complexity results also apply to other coalitional games such as skill games and matching games. The following issues are given special consideration: influence of players, limit and complexity of manipulations in the coalitional games and complexity of resource allocation on networks. The complexity of comparison of influence between players in simple games is characterized. The simple games considered are represented by winning coalitions, minimal winning coalitions, weighted voting games or multiple weighted voting games. A comprehensive classification of weighted voting games which can be solved in polynomial time is presented. An efficient algorithm which uses generating functions and interpolation to compute an integer weight vector for target power indices is proposed. Voting theory, especially the Penrose Square Root Law, is used to investigate the fairness of a real life voting model. Computational complexity of manipulation in social choice protocols can determine whether manipulation is computationally feasible or not. The computational complexity and bounds of manipulation are considered from various angles including control, false-name manipulation and bribery. Moreover, the computational complexity of computing various cooperative game solutions of simple games in dierent representations is studied. Certain structural results regarding least core payos extend to the general monotone cooperative game. The thesis also studies a coalitional game called the spanning connectivity game. It is proved that whereas computing the Banzhaf values and Shapley-Shubik indices of such games is #P-complete, there is a polynomial time combinatorial algorithm to compute the nucleolus. The results have interesting significance for optimal strategies for the wiretapping game which is a noncooperative game defined on a network

Tight Bounds for The Price of Fairness

A central decision maker (CDM), who seeks an efficient allocation of scarce resources among a finite number of players, often has to incorporate fairness criteria to avoid unfair outcomes. Indeed, the Price of Fairness (POF), a term coined in Bertsimas et al. (2011), refers to the efficiency loss due to the incorporation of fairness criteria into the allocation method. Quantifying the POF would help the CDM strike an appropriate balance between efficiency and fairness. In this paper we improve upon existing results in the literature, by providing tight bounds for the POF for the proportional fairness criterion for any $n$, when the maximum achievable utilities of the players are equal or are not equal. Further, while Bertsimas et al. (2011) have already derived a tight bound for the max-min fairness criterion for the case that all players have equal maximum achievable utilities, we also provide a tight bound in scenarios where these utilities are not equal. Finally, we investigate the sensitivity of our bounds and Bertsimas et al. (2011) bounds for the POF to the variability of the maximum achievable utilities

Distributionally robust mechanism design

We study a mechanism design problem where an indivisible good is auctioned to multiple bidders, for eachof whom it has a private value that is unknown to the seller and the other bidders. The agents perceive theensemble of all bidder values as a random vector governed by an ambiguous probability distribution, whichbelongs to a commonly known ambiguity set. The seller aims to design a revenue maximizing mechanism thatis not only immunized against the ambiguity of the bidder values but also against the uncertainty about thebidders’ attitude towards ambiguity. We argue that the seller achieves this goal by maximizing the worst-caseexpected revenue across all value distributions in the ambiguity set and by positing that the bidders haveKnightian preferences. For ambiguity sets containing all distributions supported on a hypercube, we showthat the Vickrey auction is the unique mechanism that is optimal, efficient and Pareto robustly optimal. Ifthe bidders’ values are additionally known to be independent, then the revenue of the (unknown) optimalmechanism does not exceed that of a second price auction with only one additional bidder. For ambiguitysets under which the bidders’ values are dependent and characterized through moment bounds, on the otherhand, we provide a new class of randomized mechanisms, the highest-bidder-lotteries, whose revenues cannotbe matched by any second price auction with a constant number of additional bidders. Moreover, we showthat the optimal highest-bidder-lottery is a 2-approximation of the (unknown) optimal mechanism, whereasthe best second price auction fails to provide any constant-factor approximation guarantee

A Game-Theoretic Approach to Strategic Resource Allocation Mechanisms in Edge and Fog Computing

With the rapid growth of Internet of Things (IoT), cloud-centric application management raises questions related to quality of service for real-time applications. Fog and edge computing (FEC) provide a complement to the cloud by filling the gap between cloud and IoT. Resource management on multiple resources from distributed and administrative FEC nodes is a key challenge to ensure the quality of end-user’s experience. To improve resource utilisation and system performance, researchers have been proposed many fair allocation mechanisms for resource management. Dominant Resource Fairness (DRF), a resource allocation policy for multiple resource types, meets most of the required fair allocation characteristics. However, DRF is suitable for centralised resource allocation without considering the effects (or feedbacks) of large-scale distributed environments like multi-controller software defined networking (SDN). Nash bargaining from micro-economic theory or competitive equilibrium equal incomes (CEEI) are well suited to solving dynamic optimisation problems proposing to ‘proportionately’ share resources among distributed participants. Although CEEI’s decentralised policy guarantees load balancing for performance isolation, they are not faultproof for computation offloading. The thesis aims to propose a hybrid and fair allocation mechanism for rejuvenation of decentralised SDN controller deployment. We apply multi-agent reinforcement learning (MARL) with robustness against adversarial controllers to enable efficient priority scheduling for FEC. Motivated by software cybernetics and homeostasis, weighted DRF is generalised by applying the principles of feedback (positive or/and negative network effects) in reverse game theory (GT) to design hybrid scheduling schemes for joint multi-resource and multitask offloading/forwarding in FEC environments. In the first piece of study, monotonic scheduling for joint offloading at the federated edge is addressed by proposing truthful mechanism (algorithmic) to neutralise harmful negative and positive distributive bargain externalities respectively. The IP-DRF scheme is a MARL approach applying partition form game (PFG) to guarantee second-best Pareto optimality viii | P a g e (SBPO) in allocation of multi-resources from deterministic policy in both population and resource non-monotonicity settings. In the second study, we propose DFog-DRF scheme to address truthful fog scheduling with bottleneck fairness in fault-probable wireless hierarchical networks by applying constrained coalition formation (CCF) games to implement MARL. The multi-objective optimisation problem for fog throughput maximisation is solved via a constraint dimensionality reduction methodology using fairness constraints for efficient gateway and low-level controller’s placement. For evaluation, we develop an agent-based framework to implement fair allocation policies in distributed data centre environments. In empirical results, the deterministic policy of IP-DRF scheme provides SBPO and reduces the average execution and turnaround time by 19% and 11.52% as compared to the Nash bargaining or CEEI deterministic policy for 57,445 cloudlets in population non-monotonic settings. The processing cost of tasks shows significant improvement (6.89% and 9.03% for fixed and variable pricing) for the resource non-monotonic setting - using 38,000 cloudlets. The DFog-DRF scheme when benchmarked against asset fair (MIP) policy shows superior performance (less than 1% in time complexity) for up to 30 FEC nodes. Furthermore, empirical results using 210 mobiles and 420 applications prove the efficacy of our hybrid scheduling scheme for hierarchical clustering considering latency and network usage for throughput maximisation.Abubakar Tafawa Balewa University, Bauchi (Tetfund, Nigeria