Protocol Invariance and the Timing of Decisions in Dynamic Games

We characterize a class of dynamic stochastic games that we call separable dynamic games with noisy transitions and establish that these widely used models are protocol invariant provided that periods are sufficiently short. Protocol invariance means that the set of Markov perfect equilibria is nearly the same irrespective of the order in which players are assumed to move within a period. Protocol invariance can facilitate applied work and renders the implications and predictions of a model more robust. Our class of dynamic stochastic games includes investment games, R&D races, models of industry dynamics, dynamic public construction games, asynchronously repeated games, and many other models from the extant literature

Strategic complements in two stage, 2x2 games

Strategic complements are well understood for normal form games, but less so for extensive form games. There is some evidence that extensive form games with strategic complementarities are a very restrictive class of games (Echenique (2004)). We study necessary and sufficient conditions for strategic complements (defined as increasing best responses) in two stage, 2x2 games. We find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in which payoffs satisfy these conditions has measure zero. Payoffs with these conditions require the player to be indifferent between their actions in two of the four subgames in stage two, eliminating any strategic role for their actions in these two subgames. In contrast, the set of games that exhibit strategic complements (increasing best responses) has infinite measure. This enlarges the scope of strategic complements in two stage, 2x2 games (and provides a basis for possibly greater scope in more general games). The set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice. The results are easy to apply, and are robust to including dual payoff conditions and adding a third player. Examples with several motivations are included

Strategic Exploitation of a Common-Property Resource under Uncertainty

We construct a game of noncooperative common-resource exploitation which delivers analytical solutions for its symmetric Markov-perfect Nash equilibrium. We examine how introducing uncertainty to the natural law of resource reproduction affects strategic exploitation. We show that the commons problem is always present in our example and we identify cases in which increases in risk amplify or mitigate the commons problem. For a specific class of games which imply Markov-perfect strategies that are linear in the resource stock (our example belongs to this class), we provide general results on how payoff-function features affect the responsiveness of exploitation strategies to changes in riskiness. These broader characterizations of games which imply linear strategies (appearing in an Online Appendix) can be useful in future work, given the technical difficulties that may arise by the possible nonlinearity of Markov-perfect strategies in more general settings

Dynamic nonpoint-source pollution control policy: ambient transfers and uncertainty

When a regulator cannot observe or infer individual emissions, corrective policy must rely on ambient pollution data. Assuming this kind of environment, we study a class of differential games of pollution control with profit functions that are polynomial in the global pollution stock. Given an open-loop emissions strategy satisfying mild regularity conditions, an ambient transfer scheme is exhibited that induces it in Markov-perfect equilibrium (MPE). Proposed transfers are a polynomial function of the difference between actual and desired pollution levels; moreover, they are designed so that in MPE no tax or subsidy is ever levied. Their applicability under stochastic pollution dynamics is studied for a symmetric game of polluting oligopolists with linear demand. We discuss a quadratic scheme that induces agents to adopt Markovian emissions strategies that are stationary and linearly decreasing in total pollution. Total expected ambient transfers are non-positive and their magnitude is linearly increasing in physical volatility, the size of the economy, and the absolute value of the slope of the inverse demand function. However, if the regulator is interested in inducing a constant emissions strategy then, in expectation, transfers vanish. The total expected ambient transfer is compared to its point-source equivalent

Endogenous correlated network dynamics

We model the structure and strategy of social interactions prevailing at any point in time as a directed network and we address the following open question in the theory of social and economic network formation: given the rules of network and coalition formation, preferences of individuals over networks, strategic behavior of coalitions in forming networks, and the trembles of nature, what network and coalitional dynamics are likely to emerge and persist. Our main contributions are to formulate the problem of network and coalition formation as a dynamic, stochastic game and to show that: (i) the game possesses a correlated stationary Markov equilibrium (in network and coalition formation strategies), (ii) together with the trembles of nature, this correlated stationary equilibrium determines an equilibrium Markov process of network and coalition formation, and (iii) this endogenous Markov process possesses a finite set of ergodic measures, and generates a finite, disjoint collection of nonempty subsets of networks and coalitions, each constituting a basin of attraction. Moreover, we extend to the setting of endogenous Markov dynamics the notions of pairwise stability (Jackson-Wolinsky, 1996) and the path dominance core (Page-Wooders, 2009a). We show that in order for any network-coalition pair to emerge and persist, it is necessary that the pair reside in one of finitely many basins of attraction. The results we obtain here for endogenous network dynamics and stochastic basins of attraction are the dynamic analogs of our earlier results on endogenous network formation and strategic basins of attraction in static, abstract games of network formation (Page and Wooders, 2009a), and build on the seminal contributions of Jackson and Watts (2002), Konishi and Ray (2003), and Dutta, Ghosal, and Ray (2005)

Essays on endogenous time preference and strategic interaction

Ankara : The Department of Economics, İhsan Doğramacı Bilkent Univ., 2013.Thesis (Ph. D.) -- Bilkent University, 2013.Includes bibliographical refences.This thesis includes three self contained essays on the existence and qualitative properties of equilibrium dynamics under endogenous time preference. In the Örst essay, we reconsider the optimal growth model proposed by Stern (2006). We prove the almost everywhere di§erentiability of the value function and uniqueness of the optimal path, which were left as open questions and show how a small perturbation to the price of future oriented capital qualitatively changes the equilibrium dynamics. Almost none of the studies on endogenous time preference consider the strategic interaction among the agents. In the second essay, by considering a strategic growth model with endogenous time preference, we provide the su¢ cient conditions of supermodularity for dynamic games with open-loop strategies and show that the stationary state Nash equilibria tend to be symmetric. We numerically show that the initially rich can pull the poor out of poverty trap even when sustaining a higher level of steady state capital stock for itself. Lastly, in the third essay, we consider the socially determined time preference which depends on the level of Ösh stock and characterize the basic Öshery model under this setup. We provide existence of collusive and open-loop Nash equilibria and compare the e¢ ciency and qualitative properties of them.Turan, Agah RehaPh.D

Self-Aware Transport of Heterogeneous Agents in Incomplete Markets

The present paper was prompted by the surprising discovery that the common strategy, adopted in a large body of research, for producing time-invariant equilibrium in the classical Aiyagari-Bewley-Huggett model fails to achieve its objective in a widely cited benchmark study, with the implication that, contrary to the common belief, a central problem in macroeconomics has been without an adequate solution, save for special cases. It is shown that equilibria in such models can be obtained generically only if prices, optimal policy, and population distribution are allowed to adjust toward their steady-state regimes simultaneously, which requires new modeling and computational tools. By expanding the approach proposed by Dumas and Lyasoff [11] the paper provides such tools and offers a new interpretation of problems commonly stated as mean field games or transportation of mass problems. The scope of the approximate aggregation conjecture of Krusell and Smith [19] is clarified and a new analytical technique for models with common noise is developed. The proposed new method does not resort on the representative agent framework, does not involve simulation, does not postulate infinite time horizon, and allows for disparity in the cross-section of households to be accounted for.Comment: 50 pages, 16 figure

On competition for spatially distributed resources in networks: an extended version

We study the dynamics of the exploitation of a natural resource distributed among and flowing between several nodes connected via a weighted, directed network. The network represents both the locations and the interactions of the resource nodes. A regulator decides to designate some of the nodes as natural reserves where no exploitation is allowed. The remaining nodes are assigned (one-to-one) to players, who will exploit the resource at the node. We show how the equilibrium exploitation and the resource stocks depend on the productivity of the resource sites, on the structure of the connections between the sites, and on the number and the preferences of the agents. The best locations to host nature reserves are identified according to the model’s parameters, and we find that they correspond to the most central (in the sense of eigenvector centrality) nodes of a suitably redefined network that considers the nodes’ productivity