Equilibrium in Labor Markets with Few Firms

We study competition between firms in labor markets, following a combinatorial model suggested by Kelso and Crawford [1982]. In this model, each firm is trying to recruit workers by offering a higher salary than its competitors, and its production function defines the utility generated from any actual set of recruited workers. We define two natural classes of production functions for firms, where the first one is based on additive capacities (weights), and the second on the influence of workers in a social network. We then analyze the existence of pure subgame perfect equilibrium (PSPE) in the labor market and its properties. While neither class holds the gross substitutes condition, we show that in both classes the existence of PSPE is guaranteed under certain restrictions, and in particular when there are only two competing firms. As a corollary, there exists a Walrasian equilibrium in a corresponding combinatorial auction, where bidders' valuation functions belong to these classes. While a PSPE may not exist when there are more than two firms, we perform an empirical study of equilibrium outcomes for the case of weight-based games with three firms, which extend our analytical results. We then show that stability can in some cases be extended to coalitional stability, and study the distribution of profit between firms and their workers in weight-based games

Distributed Task Management in Cyber-Physical Systems: How to Cooperate under Uncertainty?

We consider the problem of task allocation in a network of cyber-physical systems (CPSs). The network can have different states, and the tasks are of different types. The task arrival is stochastic and state-dependent. Every CPS is capable of performing each type of task with some specific state-dependent efficiency. The CPSs have to agree on task allocation prior to knowing about the realized network's state and/or the arrived tasks. We model the problem as a multi-state stochastic cooperative game with state uncertainty. We then use the concept of deterministic equivalence and sequential core to solve the problem. We establish the non-emptiness of the strong sequential core in our designed task allocation game and investigate its characteristics including uniqueness and optimality. Moreover, we prove that in the task allocation game, the strong sequential core is equivalent to Walrasian equilibrium under state uncertainty; consequently, it can be implemented by using the Walras' tatonnement process

A Day Ahead Market Energy Auction for Distribution System Operation

In this paper, we study a day ahead double energy auction in a distribution system involving dispatchable generation units, renewable generation units supported by battery storage systems(BSSs), fixed loads, price responsive loads, and supply from the Whole Sale Market(WSM) at Locational Marginal Price(LMP). The auction is implemented within a Distribution System Operator (DSO) premises using Mixed Integer Linear Programming (MIP). The proposed auction is cleared at the Distribution LMP (DLMP) and is observed to be weakly budget balanced if no penalty is applied for DSO's deviation from originally committed supply from the WSM. Furthermore, the dynamics of LMP and DLMP, and their effect on distribution market participants scheduled quantities as well as the WSM supply to the distribution system is investigated.Comment: Electro Information Technology (EIT), 2017 IEEE International Conference o

Information requirements for strategic decision making: energy market

Over the last two decades, the electricity sector has been involved in a challenging restructuring process in which the vertical integrated structure (monopoly) is being replaced by a horizontal set of companies. The growing supply of electricity, flowing in response to free market pricing at the wellhead, led to increased competition. In the new framework of deregulation, what characterizes the electric industry is a commodity wholesale electricity marketplace. This new environment has drastically changed the objective of electricity producing companies. In the vertical integrated industry, utilities were forced to meet all the demand from customers living in a certain region at fixed rates. Then, the operation of the Generation Companies (GENCOs) was centralized and a single decision maker allocated the energy services by minimizing total production costs. Nowadays, GENCOs are involved not only in the electricity market but also in additional markets such as fuel markets or environmental markets. A gas or coal producer may have fuel contracts that define the production limit over a time horizon. Therefore, producers must observe this price levels in these other markets. This is a lesson we learned from the Electricity Crisis in California. The Californian market\u27s collapse was not the result of market decentralization but it was triggered by other decisions, such as high natural gas prices, with a direct impact in the supply-demand chain. This dissertation supports generation asset business decisions -from fuel supply concerns to wholesale trading in energy and ancillary services. The forces influencing the value chain are changing rapidly, and can become highly controversial. Through this report, the author brings an integrated and objective perspective, providing a forum to identify and address common planning and operational needs. The purpose of this dissertation is to present theories and ideas that can be applied directly in algorithms to make GENCOs decisions more efficient. This will decompose the problem into independent subproblems for each time interval. This is preferred because building a complete model in one time is practically impossible. The diverse scope of this report is unified by the importance of each topic to understanding or enhancing the profitability of generation assets. Studies of top strategic issues will assess directly the promise and limits to profitability of energy trading. Studies of ancillary services will permit companies to realistically gauge the profitability of different services, and develop bidding strategies tuned to competitive markets

Sequential auctions and resale

In this thesis I study a market comprised of a sequence of auctions where buyers can choose to later resell any object they now buy. I develop a structural model of such a market and show how the possibility to resell shapes equilibrium strategies. I then estimate the model on data from classic car auctions. The model admits aggregate shocks to buyer and seller wealth and that way matches the positive empirical correlation between prices and the state of the economy. Using a separate two-period model I show analytically that the resale option may increase average prices as compared to an otherwise identical market without resale. The same two-period model shows that with aggregate shocks resale may amplify price volatility. I then evaluate the quantitative importance of these effects in a number of counterfactual experiments on the estimated model. Resale raises prices moderately but does not lead to meaningfully more volatility. Allowing (counterfactually) for instantaneous resale increases average prices and their volatility substantially. A second set of counterfactuals reveals that centralizing trade lowers prices and increases the volume of trade, thereby increasing the efficiency of the market. Price volatility remains unchanged in this scenario, even with frequent resale opportunities. An assumption in my model and several others in the literature is that bidders take a stationary distribution of rival bids as given and don't learn about that distribution from one auction to the next. This is different from the canonical model of sequential auctions in Weber (1983), where learning is present. I therefore compare the Weber model to a model where bidders face a stationary distribution of rival bids in each period. I show how equilibrium strategies differ in the two games and show that despite the differences, the two games yield the same expected prices and payoffs

Distributed optimisation techniques for wireless networks

Alongside the ever increasing traffic demand, the fifth generation (5G) cellular network architecture is being proposed to provide better quality of service, increased data rate, decreased latency, and increased capacity. Without any doubt, the 5G cellular network will comprise of ultra-dense networks and multiple input multiple output technologies. This will make the current centralised solutions impractical due to increased complexity. Moreover, the amount of coordination information that needs to be transported over the backhaul links will be increased. Distributed or decentralised solutions are promising to provide better alternatives. This thesis proposes new distributed algorithms for wireless networks which aim to reduce the amount of system overheads in the backhaul links and the system complexity. The analysis of conflicts amongst transmitters, and resource allocation are conducted via the use of game theory, convex optimisation, and auction theory. Firstly, game-theoretic model is used to analyse a mixed quality of service (QoS) strategic non-cooperative game (SNG), for a two-user multiple-input single-output (MISO) interference channel. The players are considered to have different objectives. Following this, the mixed QoS SNG is extended to a multicell multiuser network in terms of signal-to-interference-and-noise ratio (SINR) requirement. In the multicell multiuser setting, each transmitter is assumed to be serving real time users (RTUs) and non-real time users (NRTUs), simultaneously. A novel mixed QoS SNG algorithm is proposed, with its operating point identified as the Nash equilibrium-mixed QoS (NE-mixed QoS). Nash, Kalai-Smorodinsky, and Egalitarian bargain solutions are then proposed to improve the performance of the NE-mixed QoS. The performance of the bargain solutions are observed to be comparable to the centralised solutions. Secondly, user offloading and user association problems are addressed for small cells using auction theory. The main base station wishes to offload some of its users to privately owned small cell access points. A novel bid-wait-auction (BWA) algorithm, which allows single-item bidding at each auction round, is designed to decompose the combinatorial mathematical nature of the problem. An analysis on the existence and uniqueness of the dominant strategy equilibrium is conducted. The BWA is then used to form the forward BWA (FBWA) and the backward BWA (BBWA). It is observed that the BBWA allows more users to be admitted as compared to the FBWA. Finally, simultaneous multiple-round ascending auction (SMRA), altered SMRA (ASMRA), sequential combinatorial auction with item bidding (SCAIB), and repetitive combinatorial auction with item bidding (RCAIB) algorithms are proposed to perform user offloading and user association for small cells. These algorithms are able to allow bundle bidding. It is then proven that, truthful bidding is individually rational and leads to Walrasian equilibrium. The performance of the proposed auction based algorithms is evaluated. It is observed that the proposed algorithms match the performance of the centralised solutions when the guest users have low target rates. The SCAIB algorithm is shown to be the most preferred as it provides high admission rate and competitive revenue to the bidders

Network capacity enhancement in HetNets using incentivized offloading mechanism

This work investigates distributed algorithms for joint power allocation and user association in heterogeneous networks. We propose auction-based algorithms for offloading macrocell users (MUs) from the macrocell base station (MBS) to privately owned small-cell access points (SCAs). We first propose a simultaneous multiple-round ascending auction (SMRA) for allocating MUs to SCAs. Taking into account the overheads incurred by SCAs during valuation in the SMRA, further improvements are proposed using techniques known as sub-optimal altered SMRA (ASMRA), the combinatorial auction with item bidding (CAIB) and its variations; the sequential CAIB (SCAIB) and the repetitive CAIB (RCAIB). The proof for existence of the Walrasian equilibrium (WE) is demonstrated through establishing that the valuation function used by the SCAs is a gross substitute. Finally, we show that truthful bidding is individual rational for all of our proposed algorithms

Why Every Economist Should Learn Some Auction Theory

This is an Invited paper for the World Congress of the Econometric Society held in Seattle in August 2000. We discuss the strong connections between auction theory and "standard" economic theory, and argue that auction-theoretic tools and intuitions can provide useful arguments and insights in a broad range of mainstream economic settings that do not, at first sight, look like auctions. We also discuss some more obvious applications, especially to industrial organization.Auctions, Bidding, Auction Theory, Private Values, Common Values, Mechanism Design, Litigation, Stock Markets, Queues, Financial Crashes, Brand Loyalty, War of Attrition, Bertrand, Perfect Competition, E-Commerce, Spectrum Auctions, Treasury Auctions, Electricity