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In recent years, the ever-increasing research interest in various aspects of the electricity pool-based markets has generated a plethora of complementarity-based approaches to determine participating agents’ optimal offering/bidding strategies and model players’ interactions. In particular, the integration of multiple and diversified market agents, such as conventional generation companies, renewable energy sources, electricity storage facilities and agents with a mixed generation portfolio has instigated significant competition, as each player attempts to establish their market dominance and realize substantial financial benefits. The employment of complementarity modelling approaches can also prove beneficial for the optimal coordination of the electricity and natural gas market coupling. Linear and nonlinear programming as well as complementarity modelling, mainly in the form of mathematical programs with equilibrium constraints (MPECs), equilibrium programs with equilibrium constraints (EPECs) and conjectural variations models (CV) have been widely employed to provide effective market clearing mechanisms, enhance agents’ decision-making process and allow them to exert market power, under perfect and imperfect competition and various market settlements. This work first introduces the theoretical concepts that regulate the majority of contemporary competitive electricity markets. It then presents a comprehensive review of recent advances related to complementarity-based modelling methodologies and their implementation in current competitive electricity pool-based markets applications.

This paper extends the human migration model introduced in previous works to the framework of consistent conjectural variations. First, we introduce the standard multiclass human migration network equilibrium model that describes the movement of migrants between locations. Next, we introduce the concept of conjectural variations, in which migrants conjecture about the (expected) utility of locations after their migration. We define the concept of conjectural variations equilibrium and present results regarding the conditions for its existence and uniqueness. Following that, we define the concept of consistency for the migrants’ conjectures and the consistent conjectural variations equilibrium (CCVE). Finally, we describe the conditions that guarantee the existence of the CCVE.

We consider a general model of financial flows and prices with multiple sectors and instruments. Each sector optimizes the composition of assets and liabilities in its portfolio, whose utility is given by a quadratic function constrained to satisfy the accounting identity that appears in flow-of-funds accounts and the equilibrium conditions that guarantee market clearance. To define the financial equilibrium, we make use of the concept of conjectural variations, in which each sector conjectures the possible dependence of the instruments’ prices upon its portfolio structure. The problem is modeled as a continuous two-stage game. In the first stage, the set of strategies for each sector consists of its possible conjectures about its influence on the prices. The second stage is the financial model’s equilibrium problem where, according to the conjectures selected in the first stage, each sector decides its portfolio composition. Each sector aims to minimize the risks, while at the same time maximizing the value of its assets and minimizing the value of its liabilities.

We keep investigating the properties of consistent conjectural variations equilibrium (CCVE) developed for a single-commodity oligopoly. Although, in general, the consistent conjectures are distinct from those of Cournot-Nash, in our previous papers, we established the following remarkable fact. Define a meta-model as such where the players are the same agents as in the original oligopoly but now using the conjectures as their strategies. Then the Cournot-Nash equilibrium in the meta-model generated the consistent conjectural variations equilibrium in the original oligopoly. In this paper, we study the conditions under which the inverse is also true, that it, every consistent CVE provides for the Cournot-Nash optimal strategies for the meta-model. This equivalence allows one to extend the concept of CCVE to other kinds of economic and financial models lacking the oligopoly structure.

In the standard model of voluntary public good provision and other game theoretic models, climate-friendly leadership of a country is not successful: A unilateral increase of this country’s greenhouse gas abatement measures, i.e., contributions to the global public good of climate protection, will not lead to a positive reaction by the other countries but instead trigger a reduction of their abatement efforts and thus a crowding-out effect. In this paper it is shown how this undesired consequence need no longer occur when elements of behavioral economics are incorporated in the otherwise standard model of public good provision. In particular, strategic complementarities between the public good contribution of the leading country and those of the follower may result either if the follower has specific non-egoistic or other-regarding preferences or if the leader’s contribution positively affects the follower’s beliefs, i.e., his conjectural variations, about the leader’s behaviour.

This paper considers a noncooperative game of quantity competition among firms in an oligopoly market under general demand and cost functions. Each firm’s optimal response to the strategies of other firms is assessed by the magnitude and sign of its conjectural variation, expressing the firm’s expectation regarding the counterparty’s supply quantity change in response to the firm’s unit change in its supply quantity. A game of n firms with the sum of conjectural variations (SCV) regarding all counterparties as the generalized response characteristic is studied. The existence of a bifurcation of the players' response is revealed; a bifurcation is a strategy profile of the game in which both positive and negative responses are possible with an infinite-magnitude SCV value. Methods are developed for calculating the SCV value under different types of inverse demand functions (linear and power) and cost functions (linear, power, and quadratic), and the impact of these characteristics of firms on the bifurcation state is comparatively analyzed.

One of the most important problems of game theory—the game of firms in an oligopoly market—is considered. The survey covers classical and modern formulations for the game-theoretic problem of choosing optimal player’s strategies and the recent methodological achievements in oligopoly games with applications, including publications over the past five years.

The work presented in this article proposes an original method that models the medium-term market equilibrium under imperfect competition circumstances in multi-area electricity systems. It provides a system analysis considering multiple market splitting possibilities, where local market power may appear according to the status of the interconnections. As a result of new policies and regulations, power systems are increasingly integrating the existing electricity markets in unified frameworks. The integration of electricity markets poses highly challenging tasks due to the uncertainty that comes from the agents’ strategic behaviors which depend on multiple factors, for instance, the state of the interconnections. When it comes to modeling these effects, the purpose is to identify each strategy by using conjectured-price responses that depend on the different states of the system. Consequently, the problem becomes highly combinatorial, which heightens its size as well as its complexity. Therefore, the purpose of this work’s methodology is the reduction of the possible network configurations so as to ensure a computational tractability in the problem. In order to validate this methodology, it has been put to the test in a realistic and full-scale two-year operation planning model of the European electricity market that consists of a group of nine countries.

When the 1968 Merger Guidelines were drafted, both the economics and antitrust literatures addressed how competition could be softened when oligopolists anticipated the natural and predictable responses of their rivals to their competitive moves, such as price cuts or output expansion. But when economists developed new models of oligopoly behavior, and of coordinated effects in particular, the older ideas were dropped—until the 2010 Guidelines, when the older ideas were reincorporated along with the newer ones. Our article points out limitations of the work-horse repeated game model of oligopoly conduct for analyzing coordinated effects of mergers, and suggests ways to make that model more realistic. We also identify important research questions that are raised when attempting to account for oligopolists’ natural and predictable responses in evaluating the consequences of mergers, and suggest studying Stackelberg reactions as a way to make progress in doing so.

The presence of nonzero conjectural variations in pollution abatement and output make emission taxes less effective with respect to reducing emissions. This has implications for the characterization of the optimal emission tax, particularly in an international context where there are large asymmetries in pollution intensities. A higher degree of collusion in output between polluting firms results in higher emissions taxes in the non-cooperative equilibrium. In contrast, a higher degree of collusion in abatement between polluting firms results in lower emissions taxes in the non-cooperative equilibrium. These results rely on the presence of nonzero conjectural variations and large asymmetries in pollution intensities across countries. The analysis is relevant to the design of international environmental policy, including cases where countries face increasing global competition and damages from rising global emissions.