# Land Use with Contract

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This Demonstration explores an abstract evolving world in which plots of land each with two potential uses lie on a one-dimensional periodic lattice. The payoff each landowner receives on each iteration is a function of its choice of how to use its land coupled with the choices of its immediate neighbors. However, each landowner is permitted to contract without cost with a certain number of its neighbors to bind themselves to a pattern of land use. A group of five contiguous landowners can bind themselves, for example, to choose on each iteration the pattern of land use that maximizes their total payoff, given the land use choices of the neighboring noncontracting land users. They can agree to split their total payoff such that each would receive at least as much as if they did not cooperate.

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Contributed by: Seth J. Chandler (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

An interesting issue to pursue is the relationship between contract size and average payoffs. If, for example, average payoff rapidly approaches an asymptotic value as contract size increases, private land use arrangements such as covenants running with the land or private covenants may be sufficient to achieve sensible use of land without a need for government intervention such as zoning. If, however, average payoff only slowly approaches the global maximum that could theoretically be achieved were all landowners parties to a contract, government intervention would have greater warrant due to the significant costs of contracting with a large number of people.

Where the lattice size is evenly divisible by the number of parties to each contract, the system described in this Demonstration can likely be emulated by a cellular automaton with a smaller lattice and a high number of colors. There are similarities between the system described in this Demonstration and a block cellular automaton.

The *Mathematica* code underlying this Demonstration is written in a way such that it can readily be extended to situations in which the payoffs each landowner receives are a function of its behavior and a broader set of neighbors.

## Permanent Citation

"Land Use with Contract"

http://demonstrations.wolfram.com/LandUseWithContract/

Wolfram Demonstrations Project

Published: March 7 2011