Incomplete Information Model Research Articles

Modeling 'Massive Retaliation'

A generic asymmetric two-stage escalation model of incomplete information is used to examine strategic relationships in which one player adopts a defense posture akin to the “Massive Retaliation” policy of the Eisenhower administration that relies only on the threat of escalation to deter aggression. In the model, a challenger must decide whether to contest the status quo and a defender must choose between capitulation and escalation. Each player has probabilistic knowledge of the other's preference between conceding and fighting an all-out war. All perfect Bayesian equilibria of the Incomplete Information Escalation game are identified and interpreted. Unlike two-stage games of complete information, war and escalation may be rational outcomes under incomplete information. At certain times, these outcomes may be inevitable. Challengers preferring conflict to capitulation always initiate conflict, whatever the information state of the game. But when information is incomplete, even challengers with an aversion to all-out war may rationally precipitate a crisis. Similarly, when it is unsure of a challenger's preferences, even a defender preferring not to wage war may rationally choose to escalate a conflict. The conditions associated with a stable status quo, a successful challenge, an escalated conflict, and war are discussed.

Inferring null join dependencies in relational databases

The inference problem for data dependencies in relational databases is the problem of deciding whether a set of data dependencies logically implies another data dependency. For join dependencies (JDs), the inference problem has been extensively studied by utilising the well-known chase procedure. We generalise JDs to null join dependencies (NJDs) that hold in relations which may contain null values. In our model for incomplete information we allow only a single unmarked null value denoted bynull. This allows us to solve the inference problem for NJDs by extending the chase procedure to the or-chase procedure. In order to define the or-chase procedure we generalise relations with nulls to or-relations which contain a limited form of disjunctive information. The main result of the paper shows that the inference problem for NJDs, including embedded NJDs (which are a special case of NJDs), is decidable; this is realised via the or-chase procedure.

A Bargaining Model Where Parties Make Errors

IN A NOW CLASSICAL PAPER, Nash (1953) studied the following bilateral bargaining game: The two parties state their demands simultaneously. If these are compatible with a feasible agreement, each party gets the utility corresponding to his demand. Otherwise both parties get their conflict payoffs. Under quite general conditions this game has a continuum of equilibria: Any possible agreement which is both Pareto optimal and individually rational corresponds to a particular equilibrium point. Recently, the literature on sealed-bid double auctions (see, e.g., Leininger et al. (1989) and Matthews and Postlewaite (1989)) has extended Nash's model to the case where each party has incomplete information about the other party's valuation. A common feature of these models is that they lead to an even larger set of equilibria and, thus, to an aggravation of the nonuniqueness problem. In the present paper, we will show that this problem all but disappears if a different kind of uncertainty is introduced into Nash's model, viz. if one assumes that the parties make errors in choosing their actions in the bargaining process. This modification will be seen to imply the existence of an equilibrium which Pareto-dominates all other equilibria. The rationale for our assumption lies in the implausibly precise coordination needed to induce equilibrium play in Nash's original model: each (nontrivial) equilibrium consists of a pair of demands that are just compatible. Even an arbitrarily small deviation (in the wrong direction) will reduce both players to their conflict payoffs. By adding error terms to tne bids, we get rid of this discontinuity and force the players to weigh their demands against the risk of breakdown. Thus, our assumption could be seen as a way of accounting for the strategic uncertainty which seems practically unavoidable in a game where strategies are continuously variable. More fundamentally, the errors may be thought to reflect the presence of some uncertainty about the exact values of relevant parameters. Formally, the errors will be modeled by letting a player's bid result from the addition of a stochastic term to his strategy. The rules of Nash's game will also be modified by allowing a surplus to be divided between the players. While in Nash's model the players get precisely what they have demanded even when demands are more than compatible, we make the more general assumption that some fraction (ranging between zero and one) of the unclaimed surplus is divided between the parties according to a surplus partition rule. A similar assumption is made in the above-mentioned incomplete information models, but the severe indeterminacy makes it impossible to assess its influence. The above described equilibrium properties of our model hold for errors of arbitrary magnitude. Naturally, it is particularly interesting to study the properties when errors go to zero. In the special case where no surplus is divided, we find a convergence to the

The Nested Relation Type Model: An Application of Domain Theory to Databases

To date most previous approaches to incomplete information within the relational model depend on the specific semantics of the null types incorporated into this model. Herein we propose a model for incomplete information in nested relational databases which is independent of the semantics of the null types pertaining to incomplete information. Thus, the proposed model, called the nested relation type (NRT) model, allows, in addition to system-defined null types, user-defined null types. The NRT model extends the nested relational model by incorporating a form of built-in inheritance. This allows us to define a partial order between nester-relations types and a partial order between the data values of these types. By utilizing these partial orders, we define an instance, over a NRT, to be incomplete when its information content may increase. In addition, we define an algebra for the NRT model, called the NRT algebra, which is shown to supersede known algebras for relations with nulls and for nested relations by showing faithfulness to these algebras. We then investigate the monotonicity of the operators of the NRT algebra, which allows us to predict how increasing or decreasing the information content of the instances in the database affects the information content of the user's view, which is constructed from an algebraic expression over the instances in the database. Finally, we enhance the expressive power of the NRT-algebra with a least fixpoint operator in order to allow users to pose recursive queries.

Two-sided matching with incomplete information about others' preferences

A great deal of progress has been made recently in the study of two-sided matching processes, modelled both as cooperative games and as strategic games with complete information. Here we consider a natural model of incomplete information, in which agents know their own preferences but may not know those of others. It is shown that results concerning dominant and dominated strategies carry over from the complete information case to the present model, but results concerning Nash equilibria do not. Some of the modelling implications of this are briefly considered.

Information acquisition in an incomplete information model of business cycle

This paper studies the consequences of allowing information acquisition in a version of Lucas-Barro incomplete information model of business cycle. We apply the information equilibrium concept to show that an agent's information acquisition is not invariant to fluctuations of price level and that it has a significant effect on the size of output-inflation tradeoff. Using the optimality criteria, developed by Muench, we find that a change in mean money growth rate does not have any real consequences and that a constant money growth rule is superior to any monetary policy that induces all the agents to be fully informed.

Sequential elections with limited information

We develop an incomplete information model of a sequence of elections in a one-dimensional policy space, where voters have no contemporaneous information about candidate positions, and candidates have no information about voter preferences. The only source of information is contemporaneous endorsement data and historical data on the policy positions of previous winning candidates. We define a notion of “stationary rational expectations equilibrium”, and show that such an equilibrium results in outcomes which are equivalent to those that would occur under full information.

Sequential Elections with Limited Information

We develop an incomplete information model of a sequence of elections in a one-dimensional policy space, where voters have no contemporaneous information about candidate positions, and candidates have no information about voter preferences. The only source of information is contemporaneous endorsement data and historical data on the policy positions of previous winning candidates. We define a notion of “stationary rational expectations equilibrium”, and show that such an equilibrium results in outcomes which are equivalent to those that would occur under full information.

Incomplete Information, Risk Shifting, and Employment Fluctuations

This paper explores one of the ways in which acceptance of the hypothesis that labor market transactions involve arrangements for shifting risk from workers to employers strengthens the case for accepting the hypothesis that incomplete information is the critical factor in producing the positive effect of aggregate demand for output on aggregate employment. The analysis shows that the introduction of risk-shifting arrangements into models of incomplete information eliminates the dependence of the relation between aggregate demand and aggregate employment on the relative strengths of the usual substitution and income effects on labor supply of perceived real wage rates or perceived real interest rates. In addition, the analysis shows that the apparent fact that workers choose an amount of risk shifting that gives them constant nominal wage rates implies that incomplete information would produce a positive effect of aggregate demand on aggregate employment. The key to these results is that risk shifting allows workers to use the value of product associated with high levels of demand to supplement the income associated with low levels of demand. Consequently, they can choose high employment instates of high demand without causing a corresponding reduction in their expected marginal utility of consumption.