# Lloyd Shapley

> American economist and mathematician

**Wikidata**: [Q244739](https://www.wikidata.org/wiki/Q244739)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Lloyd_Shapley)  
**Source**: https://4ort.xyz/entity/lloyd-shapley

## Summary
Lloyd Stowell Shapley was an American economist and mathematician renowned as a pioneer of game theory. He was a Nobel Memorial Prize laureate in Economic Sciences recognized for his foundational contributions, including the Shapley value and the Gale-Shapley algorithm.

## Biography
- **Born**: June 2, 1923
- **Died**: March 12, 2016
- **Nationality**: United States
- **Education**: Phillips Exeter Academy; Harvard University; Princeton University
- **Known for**: Foundational contributions to game theory, particularly the Shapley value and stable matching theory.
- **Employer(s)**: RAND Corporation; University of California, Los Angeles
- **Field(s)**: Mathematics; Economics; Game Theory
- **Occupations**: Economist; Mathematician; University Teacher; Statistician

## Contributions
Lloyd Shapley authored several foundational concepts and theorems in mathematics and economics:
*   **Shapley Value (1953)**: A solution concept in cooperative game theory used to fairly distribute the total gains or costs among players based on their marginal contributions.
*   **Gale-Shapley Algorithm**: An algorithm developed with David Gale for solving the stable matching problem, which has applications in market design and resource allocation.
*   **Bondareva–Shapley Theorem**: A mathematical theorem providing a necessary and sufficient condition for the non-emptiness of the core of a cooperative game.
*   **Shapley–Shubik Power Index**: A method for calculating the voting power of a player in a voting body.
*   **Shapley–Folkman Lemma**: A result in convex geometry with applications in economics and optimization.

## FAQs

**What awards did Lloyd Shapley receive?**
Shapley received the Nobel Memorial Prize in Economic Sciences, the John von Neumann Theory Prize, the Bronze Star Medal, and the Golden Goose Award.

**Where did Lloyd Shapley work and teach?**
He was a long-time researcher at the RAND Corporation and later a professor at the University of California, Los Angeles. He was also affiliated with Harvard University and Princeton University during his education.

**What professional societies was Lloyd Shapley a member of?**
He was a member of the National Academy of Sciences, the American Academy of Arts and Sciences, the American Mathematical Society, and the Econometric Society.

**Who influenced Lloyd Shapley's work?**
His work was influenced by John von Neumann, a foundational figure in game theory and computer science, as well as Martin Shubik and others in the field.

## Why They Matter
Lloyd Shapley is widely considered one of the founding fathers of game theory, a field that revolutionized economics, political science, and evolutionary biology. His theoretical work on cooperative games, particularly the Shapley value, provided the first rigorous method for fairly allocating value in collaborative settings, influencing fields ranging from cost-sharing to artificial intelligence. The Gale-Shapley algorithm solved the "stable marriage problem," which became the theoretical basis for matching residents to hospitals and students to schools. His collaboration with Martin Shubik on power indices provided essential tools for analyzing political voting systems. By bridging abstract mathematics with practical economic design, Shapley's work laid the groundwork for the field of market design, recognized decades later by the Nobel Committee.

## Notable For
- **Nobel Memorial Prize in Economic Sciences**: Awarded for his analysis of market design and matching theory.
- **Shapley Value**: The most influential solution concept in cooperative game theory.
- **Gale-Shapley Algorithm**: The foundational algorithm for stable matching problems.
- **John von Neumann Theory Prize**: Recognizing his lifetime contributions to operations research and management science.
- **Bronze Star Medal**: Awarded for his service in the United States Armed Forces.
- **National Academy of Sciences**: Elected member recognizing his distinguished achievements in original research.
- **Golden Goose Award**: Recognizing federally funded research that led to significant societal benefits.

## Body

### Early Life and Education
Lloyd Stowell Shapley was born on June 2, 1923. He attended Phillips Exeter Academy for his early education. He pursued higher education at Harvard University and later at Princeton University, where he was immersed in the emerging field of game theory.

### Academic and Professional Career
Shapley spent a significant portion of his career at the RAND Corporation, a research organization known for its contributions to game theory and systems analysis during the Cold War. Later, he joined the faculty of the University of California, Los Angeles (UCLA), where he served as a university teacher. His professional affiliations included membership in prestigious organizations such as the American Mathematical Society, the National Academy of Sciences, the American Academy of Arts and Sciences, and the Econometric Society.

### Key Contributions to Game Theory
Shapley's work fundamentally shaped the landscape of cooperative game theory.
*   **The Shapley Value**: Introduced in 1953, this concept assigns a unique distribution of a total surplus generated by the coalition of all players. It satisfies several desirable axioms (efficiency, symmetry, dummy player, and additivity) and remains a central tool in economic analysis.
*   **The Gale-Shapley Algorithm**: Developed with David Gale, this algorithm solves the problem of matching two equally sized sets of elements (such as men and women, or hospitals and residents) in a way that no two elements would prefer each other over their current partners. It guarantees a stable matching solution.
*   **Bondareva–Shapley Theorem**: Independently discovered by Olga Bondareva and Shapley, this theorem characterizes when the core of a cooperative game is non-empty using the concept of balanced collections.
*   **Shapley–Shubik Power Index**: Created with Martin Shubik, this index measures the power of a player in a voting game by counting how often the player is "pivotal" in a random ordering of players.

### Military Service and Recognition
Shapley served in the United States Armed Forces, for which he received the Bronze Star Medal. His contributions to science were later recognized with the Golden Goose Award, highlighting the impact of federally funded research.

### Legacy and Influence
Shapley's work was heavily influenced by John von Neumann, a pioneer of game theory and computer science. Shapley, in turn, influenced a generation of economists and mathematicians. His collaboration with Martin Shubik expanded the application of game theory to political science and economics. He passed away on March 12, 2016, leaving behind a legacy codified in theorems, algorithms, and indices that bear his name.

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