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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2304.08727 |
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| _version_ | 1866917559869112320 |
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| author | Hickey, Joseph |
| author_facet | Hickey, Joseph |
| contents | Firms compete for clients, creating distributions of market shares ranging from domination by a few giant companies to markets in which there are many small firms. These market structures evolve in time, and may remain stable for many years before a new firm emerges and rapidly obtains a large market share. We seek the simplest realistic model giving rise to such diverse market structures and dynamics. We focus on markets in which every client adopts a single firm, and can, from time to time, switch to a different firm. Examples include markets of cell phone and Internet service providers, and of consumer products with strong brand identification. In the model, the size of a particular firm, labelled $i$, is equal to its current number of clients, $n_i$. In every step of the simulation, a client is chosen at random, and then selects a firm from among the full set of firms with probability $p_i = (n_i^α+ β)/K$, where $K$ is the normalization factor. Our model thus has two parameters: $α$ represents the degree to which firm size is an advantage ($α$ > 1) or disadvantage ($α$ < 1), relative to strict proportionality to size ($α$ = 1), and $β$ represents the degree to which small firms are viable despite their small size. We postulate that $α$ and $β$ are determined by the regulatory, technology, business culture and social environments. The model exhibits a phase diagram in the parameter space, with different regions of behaviour. At the large $α$ extreme of the phase diagram, a single dominant firm emerges, whose market share depends on the value of $β$. At the small $α$ extreme, many firms with small market shares coexist, and no dominant firm emerges. In the intermediate region, markets are divided among a relatively small number of firms, each with sizeable market share but with distinct rankings, which can persist for long [...] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08727 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simple model of market share dynamics based on clients' firm-switching decisions Hickey, Joseph Physics and Society Theoretical Economics Firms compete for clients, creating distributions of market shares ranging from domination by a few giant companies to markets in which there are many small firms. These market structures evolve in time, and may remain stable for many years before a new firm emerges and rapidly obtains a large market share. We seek the simplest realistic model giving rise to such diverse market structures and dynamics. We focus on markets in which every client adopts a single firm, and can, from time to time, switch to a different firm. Examples include markets of cell phone and Internet service providers, and of consumer products with strong brand identification. In the model, the size of a particular firm, labelled $i$, is equal to its current number of clients, $n_i$. In every step of the simulation, a client is chosen at random, and then selects a firm from among the full set of firms with probability $p_i = (n_i^α+ β)/K$, where $K$ is the normalization factor. Our model thus has two parameters: $α$ represents the degree to which firm size is an advantage ($α$ > 1) or disadvantage ($α$ < 1), relative to strict proportionality to size ($α$ = 1), and $β$ represents the degree to which small firms are viable despite their small size. We postulate that $α$ and $β$ are determined by the regulatory, technology, business culture and social environments. The model exhibits a phase diagram in the parameter space, with different regions of behaviour. At the large $α$ extreme of the phase diagram, a single dominant firm emerges, whose market share depends on the value of $β$. At the small $α$ extreme, many firms with small market shares coexist, and no dominant firm emerges. In the intermediate region, markets are divided among a relatively small number of firms, each with sizeable market share but with distinct rankings, which can persist for long [...] |
| title | Simple model of market share dynamics based on clients' firm-switching decisions |
| topic | Physics and Society Theoretical Economics |
| url | https://arxiv.org/abs/2304.08727 |