Welfare Analysis of HIV/AIDS: Formulating and Computing a Continuous Time Overlapping Generations Policy Model

We introduce a continuous time overlapping generations demographic model, in which a social planner seeks to generate an optimal policy for influencing the demographic change of the underlying population in a neoclassical growth model. The model has the notable feature that the underlying state space is a continuum, leading to a Hamilton-Jacobi-Bellman PDE system which is defined over a Hilbert space generated by the ages of the population cohorts. In this technical report the dynamic programming problem is presented and the numerical approximation using a finite difference approximation is derived. This analysis is part of a larger research program on welfare analysis and policy development for the HIV/AIDS global pandemic.Optimal control, continuous time overlapping generations, Hamilton-Jacobi-Bellman PDE, finite difference approximation, HIV/AIDS, demographic modeling

Cross-Ownership Among Firms: Some Determinants of the Separation of Ownership from Control

This paper demonstrates that the current literature on cross-ownership among firms underestimates the true degree of separation between cash flow rights and voting rights. We use accounting identities to define coefficients of control, such that any (direct or indirect) control of a firm may be identified using these coefficients. This procedure is sufficient to show that under cross-ownership the voting rights associated with ownership are typically underestimated. We demonstrate by example that control and ownership of dividend rights may be entirely separated, and that multiple equilibria may exist in economies with cross ownership.Cross-ownership, Ownership and control, Corporate governance

Network Formation in the Political Blogosphere. An Application of Agent Based Simulation and e-Research Tools

The political blogosphere has recently been the focus of attention for social network analysis and applications of network and graph theory. In a recent paper, Adamic and Glance (2005) report differences between the linking behavior of politically conservative vs. politically liberal Web bloggers. We construct a simple agent-based network formation model which shows that one such difference, demonstrating what we term ‘political homophily’, can be generated by connecting the blogosphere to the underlying population distribution of political preferences. The model is implemented as a web service in the e-tool VOSON (Virtual Observatory for the Study of Online Networks), and both model and tool serve to define a natural environment for research into link formation behavior with large numbers of heterogeneous network participants.Network formation, Social network analysis, Blogosphere, VOSON, Agentbased simulation

From Curved Bonding to Configuration Spaces

Bonding curves are continuous liquidity mechanisms which are used in market design for cryptographically-supported token economies. Tokens are atomic units of state information which are cryptographically verifiable in peer-to-peer networks. Bonding curves are an example of an enforceable mechanism through which participating agents influence this state. By designing such mechanisms, an engineer may establish the topological structure of a token economy without presupposing the utilities or associated actions of the agents within that economy. This is accomplished by introducing configuration spaces, which are proper subsets of the global state space representing all achievable states under the designed mechanisms. Any global properties true for all points in the configuration space are true for all possible sequences of actions on the part of agents. This paper generalizes the notion of a bonding curve to formalize the relationship between cryptographically enforced mechanisms and their associated configuration spaces, using invariant properties of conservation functions. We then proceed to apply this framework to analyze the augmented bonding curve design, which is currently under development by a project in the non-profit funding sector.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Shaking the Tree: An Agency Theoretic Model of Asset Pricing

In this paper, we develop an agency-theoretic extension of the Lucas asset pricing model and examine the resulting asset price dynamics. In the model, an agent of the firm can expand or contract the firm's output and dividend payments in response to exogenous shocks, although expansions become increasingly costly for the agent to maintain. Analysis of numerical simulations shows that the time-series of equilibrium asset prices exhibits both significant time-varying conditional heteroskedasticity, and longer memory persistence.

Finite Memory Distributed Systems

A distributed system model is studied, where individual agents play repeatedly against each other and change their strategies based upon previous play. It is shown how to model this environment in terms of continuous population densities of agent types. A complication arises because the population densities of different strategies depend upon each other not only through game payoffs, but also through the strategy distributions themselves. In spite of this, it is shown that when an agent imitates the strategy of his previous opponent at a sufficiently high rate, the system of equations which governs the dynamical evolution of agent populations can be reduced to one equation for the total population. In a sense, the dynamics 'collapse' to the dynamics of the entire system taken as a whole, which describes the behavior of all types of agents. We explore the implications of this model, and present both analytical and simulation results.Fixed strategy, Prisoner's dilemma, Fokker-Plank, Distributed system

Welfare Analysis of HIV/AIDS: Formulating and Computing a Continuous Time Overlapping Generations Policy Model

Abstract: We introduce a continuous time overlapping generations demographic model, in which a social planner seeks to generate an optimal policy for influencing the demographic change of the underlying population in a neoclassical growth model. Themodel has the notable feature that the underlying state space is a continuum, leading to a Hamilton-Jacobi-Bellman PDE system which is defined over a Hilbert space generated by the ages of the population cohorts. In this technical report the dynamicprogramming problem is presented and the numerical approximation using a finite difference approximation is derived. This analysis is part of a larger research program on welfare analysis and policy development for the HIV/AIDS global pandemic.

Economic Games as Estimators

Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Functional Rational Expectations Equilibria in Market Games

Abstract: The rational expectations equilibrium has been criticized as an equilibrium concept in market game environments. Such an equilibrium may not exist generically, or it may introduce unrealistic assumptions about an economic agent's knowledgeor computational ability. We define a rational expectations equilibrium as a probability measure over uncertain states of nature which exploits all available information in a market game, and which exists for almost all economies. Furthermore, if retrading is allowed, it is possible for agents to compute such a 'functional rational expectations equilibrium' using straightforward numerical fixed point algorithms.

A PRACTICAL THEORY OF FUNGIBILITY

We formalize 'degrees of fungibility' by differentiating goods according to both their underlying attributes and the perceived value and/or usefulness of those attributes to a value assessor. This allows us to distinguish between goods that appear to be 'exactly the same' from those goods that appear to be 'nearly the same'. Such a distinction is of particular importance in the design space of digital goods, which may exist both natively in the digital space and as surrogates, i.e. as digital representations of physical goods. We provide motivating examples where digital objects are too fungible for certain desired uses, and proceed to develop a formal framework under which degrees of fungibility can be defined and characterized. We close by bridging this framework to applications in machine learning and market design.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc