Anna Rubinchik

Equilibria in an overlapping generations model with transfer policies and exogenous growth

For an overlapping generations economy with varying life-cycle productivity, non-stationary endowments, continuous time starting at

PARETO OPTIMALITY OF THE GOLDEN RULE EQUILIBRIUM IN AN OVERLAPPING GENERATIONS MODEL WITH PRODUCTION AND TRANSFERS

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The asymptotic core, nucleolus and Shapley value of smooth market games with symmetric large players

(hence allowing for full anticipation), constant-returns-to-scale production and ces utility, we fully characterise equilibria where output is higher than investment, which is strictly positive. Net assets (aggregate savings minus the value of the capital stock) are constant in any equilibrium, and, for balanced growth equilibria ( bge, defined for an economy with stationary endowments), net assets are non-zero only in the golden rule equilibrium, in accord with Gale ( 1973 ). The number of bge is finite. Their parity, however, depends on the life-cycle productivity, in particular, on the relation between the intertemporal elasticity of substitution, the minimal working age and the minimal tax age. Copyright Springer-Verlag Berlin Heidelberg 2013

Demand for contract enforcement in a barter environment

For two independent principles of intergenerational equity, the implied discount rate equals the growth rate of real per capita income, say, 2%, thus falling right into the range suggested by the U.S. Office of Management and Budget. To prove this, we develop a simple tool to evaluate small policy changes affecting several generations, by reducing the dynamic problem to a static one. A necessary condition is time invariance, which is satisfied by any common solution concept in an overlapping-generations model with exogenous growth. This tool is applied to derive the discount rate for cost–benefit analysis under two different utilitarian welfare functions: classical and relative. It is only with relative utilitarianism, and assuming time-invariance of the set of alternatives (policies), that the discount rate is well defined for a heterogeneous society at a balanced growth equilibrium, is corroborated by an independent principle equating values of human lives, and equals the growth rate of real per-capita income.

Contests with three or more heterogeneous agents

The main result is that the golden rule equilibrium (GRE) is Pareto optimal (in the classical sense) in an overlapping generations (OG) model with constant-returns-to-scale production, transfers, arbitrary life-time productivity and CES instantaneous felicity. In addition, we extend Cass and Yaaris [10] equivalence between efficiency (aggregate consumption dominance) and the present value dominance (with evaluation made using a candidate equilibrium price path).

Separate control over the local and the asymptotic behaviour in L_p spaces

Reinforcement learning describes the process by which during a series of trial-and-error attempts, actions that culminate in reward are reinforced, becoming more likely to be chosen in similar circumstances. When decisions are based on sensory stimuli, an association is formed between the stimulus, the action and the reward. Computational, behavioral and neurobiological accounts of this process successfully explain simple learning of stimuli that differ in one aspect, or along a single stimulus dimension. However, when stimuli may vary across several dimensions, identifying which features are relevant for the reward is not trivial, and the underlying cognitive process is poorly understood. To study this we adapted an intra-dimensional/ extra-dimensional set-shifting paradigm to train rats on a multi-sensory discrimination task. In our setup, stimuli of different modalities (spatial, olfactory and visual) are combined into complex cues and manipulated independently. In each set, only a single stimulus dimension is relevant for reward. To distinguish between learning and decision-making we suggest a weighted attention model (WAM). Our model learns by assigning a separate learning rule for the values of features of each dimension (e.g., for each color), reinforced after every experience. Decisions are made by comparing weighted averages of the learnt values, factored by dimension specific weights. Based on the observed behavior of the rats we estimated the parameters of the WAM and demonstrated that it outperforms an alternative model, in which a learnt value is assigned to each combination of features. Estimated decision weights of the WAM reveal an experience-based bias in learning. In the first experimental set the weights associated with all dimensions were similar. The extra-dimensional shift rendered this dimension irrelevant. However, its decision weight remained high for the early learning stage in this last set, providing an explanation for the poor performance of the animals. Thus, estimated weights can be viewed as a possible way to quantify the experience-based bias.

Essential properties of Lp,q spaces (the amalgams) and the implicit function theorem for equilibrium analysis in continuous time

We examine the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector in a transferable utility (TU) market game. We provide sufficient conditions for the asymptotic core and the nucleolus to coincide with the unique TU competitive payoff distribution. This equivalence results from nucleolus of a finite TU market game belonging to its core, the core equivalence in a symmetric oligopoly with identical atoms and single-valuedness of the core in the limiting smooth game. In some cases (but not always), the asymptotic Shapley value is more favourable for the large traders than the nucleolus, in contrast to the monopoly case (Einy et al. in J Econ Theory 89(2):186–206, 1999), where the nucleolus allocation is larger than the Shapley value for the atom.

Discounting and welfare evaluation of policies

Do greater potential gains from trade enhance or erode contracting institutions? In an anonymous exchange environment traders can sign a contract, hence agreeing to interact with the assigned partner, or wait till the next match. Any contract can be endorsed (for a payment) by the enforcement agency, which then observes the interaction with a positive probability known to the traders and punishes any detected infractors. Demand for contract enforcement is the highest amount a proposer of a contract is ready to pay to the agency, in a stationary subgame perfect equilibrium. It may be strictly positive, as we show, even when contracts are broken. Surprisingly, larger potential gains from exchange may dampen the demand, but not always: the demand is boosted under agencies that oversee the interactions frequently.