人工知能学会
経営課題にAIを！ビジネスインフォマティクス研究会 (第7回)
JSAI Special Interest Group on Business Informatics (SIG-BI #7)

࣐ࣝࢳ࢚࣮ࢪ࢙ࣥࢺࢩ࣑࣮ࣗࣞࢩࣙࣥࢆ⏝࠸ࡓ✵㛫ⓗ➇தࡢ◊✲࡟㛵ࡍࡿ᳨ウInvestigation for Spatial Competition using Multi-Agent Simulation୕ᾆᨻྖ㸪ⓑ▼⚽ኖ Masashi Miura, Hidetoshi Shiroishi㫽ྲྀ኱ᏛTottori University
Abstract: Conventionally, the research for spatial competition originating from Hotelling model has beentreated as analytic optimization problem in game situation. On the contrary, our research intends to deal
with more complex and diverse situations by introducing agent-based modeling and simulation to theresearch for spatial competition. This paper will introduce the agent simulator which we've developed as aprototype.

1. ࡣࡌࡵ࡟ᑠ኎ᴗࡢ❧ᆅ➇தࡸ〇㐀ᴗ⪅ࡢ〇ရᕪู໬࡟ࡼࡿ➇தࢆᢅ࠺✵㛫ⓗ➇தࣔࢹࣝࡢ◊✲࡛ࡣ㸪⥺ศᕷሙ࡟࠾ࡅࡿ᭱ᑠᕪู໬ཎ⌮ࢆᑟฟࡋࡓ Hotelling ࡢࣔࢹࣝ[㸯]ࢆ※ὶ࡜ࡋ࡚㸪ᵝࠎ࡞ࣔࢹࣝ໬࡜ศᯒࡀ⾜ࢃࢀ࡚ࡁࡓ㸬ᮏ◊✲࡛ࡣ㸪ࢤ࣮࣒ⓗ≧ἣ࡟࠾ࡅࡿ᭱㐺໬ၥ㢟ࢆゎᯒⓗ࡟ゎࡃ࡜࠸࠺࢔ࣉ࣮ࣟࢳ࡛⾜ࢃࢀ࡚ࡁࡓᚑ᮶ࡢ✵㛫ⓗ➇தࣔࢹࣝࡢ◊✲࡟ᑐࡋ࡚㸪࢚࣮ࢪ࢙ࣥࢺ࣮࣋ࢫ࡞ࣔࢹࣝ໬࡜ࢩ࣑࣮ࣗࣞࢩࣙࣥࢆᑟ
ධࡍࡿࡇ࡜࡛㸪ࡼࡾ」㞧࡛ከᵝ࡞≧ἣ࣭⌧㇟ࢆᢅ࠺ࡇ࡜ࢆ┠ᣦࡍ㸬

2. ࢚࣮ࢪ࢙ࣥࢺࣔࢹࣝᮏ⠇࡛ࡣ㸪⥺ศᕷሙࢆᢅࡗࡓ Hotelling ࡢࣔࢹࣝࢆ2 ḟඖ࡟ᣑᙇࡋࡓ Tabuchi ࡢࣔࢹࣝ[㸰]࡟ᇶ࡙ࡁ㸪2ḟඖᕷሙ✵㛫࡟࠾ࡅࡿ 2 ࡘࡢ௻ᴗࡢ✵㛫ⓗ➇தࡢ࢚࣮ࢪ࢙ࣥࢺࣔࢹࣝࢆ⪃࠼ࡿ㸬ࡇࡢࣔࢹࣝ࡟࠾ࡅࡿ࢚
࣮ࢪ࢙ࣥࢺࡣ㸪2 ḟඖ✵㛫(x, y)ࡢᕷሙ࡟ᆒ୍࡟ศᕸ
ࡍࡿ N ேࡢᾘ㈝⪅࡜㸪ྠࡌ✵㛫ෆ࡟❧ᆅࡋ㸪㈍኎ࡍ
ࡿྠ✀ࡢ㈈࡟ᑐࡋ࡚ࡑࢀࡒࢀ౯᱁ p1 ࡜ p2 ࢆタᐃࡋ࡚࠸ࡿ௻ᴗ 1 ࠾ࡼࡧ௻ᴗ 2 ࡛࠶ࡿ㸬

2.1 ᾘ㈝⪅ࡢ௻ᴗ㑅ᢥᕷሙ✵㛫ෆ࡟ศᕸࡍࡿྛᾘ㈝ࡣ㸪ྛ௻ᴗ࡟タᐃࡉࢀࡓ౯᱁࡜㸪⮬㌟࠿ࡽࡢ㊥㞳࡟ࡼࡗ࡚ࡑࢀࡒࢀࡢ௻
ᴗ࠿ࡽ㈈ࢆ㉎ධࡍࡿ㝿ࡢࢥࢫࢺࢆホ౯ࡋ㸪ࢥࢫࢺࡀᑠࡉ࠸᪉ࡢ௻ᴗ࠿ࡽ㈈ࢆ 1 ༢఩ࡔࡅ㉎ධࡍࡿ㸬i ␒┠ࡢᾘ㈝⪅ࡢ఩⨨ࢆ ( xic , y ic ) 㸪௻ᴗ 1 ࡜௻ᴗ 2 ࡢ❧ᆅࢆࡑࢀࡒࢀ(x1, y1)㸪(x2, y2)࡜ࡍࡿ࡜ࡁ㸪i ␒┠ࡢᾘ㈝⪅࠿ࡽぢࡓྛ௻ᴗࡢࢥࢫࢺࡣ㸪㐺ᙜ࡞ᐃᩘ t ࢆ⏝࠸࡚ୗグࡢࡼ࠺࡟࡞ࡿ࡜ࡍࡿ㸬௻ᴗࠉ
1 : ࠉp1  t ( xic  x1 ) 2  t ( yic  y1 ) 2௻ᴗࠉ
2 : ࠉp2  t ( xic  x2 ) 2  t ( yic  y2 ) 2 ୖグࡢࢥࢫࢺ㛵ᩘ࡟ᇶ࡙ࡁ඲࡚ࡢᾘ㈝⪅ࡀ௻ᴗࢆ㑅ᢥࡋࡓ⤖ᯝ㸪ྛ௻ᴗࡢ฼┈ࡣ౯᱁࡜ࡑࡢ௻ᴗࢆ㑅
ᢥࡋࡓᾘ㈝⪅ᩘࡢ✚࡜ࡋ࡚⟬ฟࡉࢀࡿ㸬ྛ௻ᴗࡣࡑࡒࢀࡢ฼┈ࢆ᭱኱໬ࡍࡿࡼ࠺ᡓ␎ⓗ࡟⾜ືࡋ㸪❧ᆅ㑅ᢥ࡜౯᱁タᐃ࠿ࡽ࡞ࡿ 2 ẁ㝵ࢤ࣮࣒ࢆ⾜࠺㸬ࡇࡇ࡛㸪2 ẁ㝵ࢤ࣮࣒ࡢ௦⾲ⓗ࡞ゎἲ࡛࠶ࡿᚋࢁྥࡁᖐ
⣡ἲ[㸱]ࢆ࣮࣋ࢫ࡜ࡋ࡚௻ᴗࡢ⾜ືࣔࢹࣝ⪃࠼ࡿ㸬

2.2 ౯᱁タᐃࡲࡎ㸪୧௻ᴗࡢ❧ᆅࢆᡤ୚࡜ࡋࡓ࡜ࡁࡢ౯᱁タᐃࢆ⪃࠼ࡿ㸬ィ⟬㈇Ⲵࢆ⪃៖ࡋ㸪௻ᴗ 1 ࡜௻ᴗ 2 ࡀྲྀࡾᚓࡿ౯᱁ࡢ⤌ࡳྜࢃࡏࡢ඲࡚࡜ࡑࢀࡒࢀ࡟࠾ࡅࡿ฼┈ࢆ⟬ฟࡍࡿ௦ࢃࡾ࡟㸪௻ᴗ 1 ࡜௻ᴗ 2 ࡀ஺஫࡟౯᱁ࢆ᭦᪂ࡋ㸪᭦᪂࡟ࡼࡿ౯᱁ኚ໬ࡀ୍ᐃࡢ⠊ᅖ࡟཰ࡲࡗࡓ࡜ࡇࢁࢆᆒ⾮≧ែ࡜ࡋ࡚ᢅ࠺㸬ࡇࡢ࡜ࡁ㸪ᾘ㈝⪅࢚࣮ࢪ࢙ࣥࢺ࠿ࡽぢࡓ␃ಖ౯᱁ࢆ᭦᪂౯᱁ࡢೃ⿵࡜ࡍࡿࡇ࡜࡛㸪ᑡ࡞࠸ࢫࢸࢵࣉᩘ࡛ᆒ⾮≧ែ࿘㎶࡟฿㐩ࡍࡿࡼ࠺ᕤኵࡍࡿ㸬௻ᴗ 1 ࡢ౯᱁ࢆ᭦᪂ࡍࡿ࡜ࡁ࡟ࡣ㸪ࡲࡎ௻ᴗ 2 ࡢ౯᱁ࢆᅛᐃࡋࡓ࡜ࡁࡢྛᾘ㈝⪅࠿ࡽぢࡓ௻ᴗ 1 ࡟ᑐࡍࡿ␃ಖ౯᱁㸪ࡍ࡞ࢃࡕ௻ᴗ 1 ࢆ㑅ᢥࡍࡿୖ㝈ࡢ౯᱁ࢆ⟬ฟࡍࡿ㸬ࡇ࠺ࡋ࡚ᚓࡽࢀࡓ␃ಖ౯᱁ࡢ㞟ྜࢆ௻ᴗ 1 ࡀ࡜ࡿ౯᱁ࡢೃ⿵࡜ࡋ࡚฼┈ィ⟬ࢆ⾜࠸㸪᭱ࡶ㧗࠸฼┈ࢆ୚࠼ࡿ౯᱁

人工知能学会
経営課題にAIを！ビジネスインフォマティクス研究会 (第7回)
JSAI Special Interest Group on Business Informatics (SIG-BI #7)

ࢆ௻ᴗ 1 ࡢ᭦᪂౯᱁࡜ࡋ࡚᥇⏝ࡍࡿ㸬ྠᵝ࡟ࡋ࡚௻ᴗ 2 ࡢ౯᱁᭦᪂ࢆ⾜࠸㸪᭦᪂࡟ࡼࡿ౯᱁ኚ໬ࡀ୍ᐃ
ࡢ⠊ᅖ࡟཰ࡲࡿࡲ࡛ࡑࢀࢆ⧞ࡾ㏉ࡍ㸬

2.3 ❧ᆅ㑅ᢥḟ࡟㸪❧ᆅࡢ㑅ᢥࢆ⪃࠼ࡿ㸬඲࡚ࡢ࠶ࡾᚓࡿ❧ᆅࡢ⤌ࡳྜࢃࡏࢆㄪ࡭ࡿ௦ࢃࡾ࡟㸪ᕷሙ✵㛫ࡢ୰࡟ Nsಶࡢ❧ᆅೃ⿵Ⅼࢆྲྀࡾ㸪௻ᴗࡀ஺஫࡟❧ᆅ㑅ᢥࢆ⧞
ࡾ㏉ࡍ࡜ࡍࡿ㸬ࡲࡎ㸪௻ᴗ 2 ࡢ❧ᆅࢆᅛᐃࡋࡓ࡜ࡁ
࡟௻ᴗ 1 ࡀ❧ᆅࢆ㑅ᢥࡍࡿ㸬ࡇࡢ࡜ࡁ㸪❧ᆅ࡜࡞ࡿೃ⿵ࡢⅬࡢࡑࢀࡒࢀ࡟ᑐࡋ㸪௻ᴗ 1 ࡀࡑࡢⅬࢆ㑅ᢥࡋࡓ≧ἣୗ࡛ 2.2 ⠇࡟♧ࡋࡓ౯᱁タᐃࣉࣟࢭࢫࢆ⾜࠺㸬඲࡚ࡢ❧ᆅೃ⿵Ⅼ࡟ᑐࡋ࡚౯᱁タᐃࣉࣟࢭࢫࢆᐇ⾜ࡋࡓᚋ㸪௻ᴗ 1 ࡟᭱ࡶ㧗࠸฼┈ࢆ୚࠼ࡿೃ⿵Ⅼࢆ❧ᆅⅬ࡜ࡋ࡚᥇⏝ࡋ㸪ࡑࡢ࡜ࡁࡢ౯᱁タᐃ⤖ᯝ࡜ࡋ࡚ᚓࡽࢀࡿᆒ⾮≧ែࡢ౯᱁ࢆ㸪௻ᴗ 1 ࠾ࡼࡧ௻ᴗ2 ࡢ౯᱁࡜ࡋ࡚タᐃࡍࡿ㸬ࡇ࠺ࡋ࡚㑅ᢥࡉࢀࡓ௻ᴗ 1ࡢ❧ᆅ࡟ᑐࡋ࡚㸪ྠᵝࡢࣉࣟࢭࢫ࡛௻ᴗ 2 ࡀ❧ᆅࢆ㑅ᢥࡍࡿ㸬௻ᴗࡀࡇࡢࡼ࠺࡞஺஫ࡢ❧ᆅ㑅ᢥ࡜౯᱁タᐃࢆ⧞ࡾ㏉ࡍࡇ࡜࡛ࢩ࣑࣮ࣗࣞࢩࣙࣥࡀ㐍⾜ࡍࡿ㸬ࢩ࣑࣮ࣗࣞࢩࣙࣥ඲యࡢὶࢀࢆᅗ 2 ࡟♧ࡍ㸬

3. ࢩ࣑࣮ࣗࣞࢩࣙࣥ ๓⠇࡛♧ࡋࡓࡼ࠺࡞ᙧ࡛࢚࣮ࢪ࢙ࣥࢺࣔࢹࣝ࡬࡜
ᣑᙇࡋࡓ 2 ḟඖ✵㛫➇தࣔࢹࣝࢆ⏝࠸࡚㸪࣐ࣝࢳ࢚࣮ࢪ࢙ࣥࢺࢩ࣑࣮ࣗࣞࢩࣙࣥࢆᵓ⠏ࡋࡓ㸬ᅗ 2 ࡟ࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝࡢ୍౛ࢆ♧ࡍ㸬㟷࡜㉥ࡢᅄゅࡢ࣐࣮࣮࢝ࡀࡑࢀࡒࢀ௻ᴗ 1 ࡜௻ᴗ 2 ࢆ⾲ࡍ㸬Ⅼ⥺ࡣ㸪ྛᾘ㈝⪅࡜㸪ࡑࢀࡒࢀࡀ㑅ᢥࡋࡓ௻ᴗࢆ⤖ࡪࡶࡢ࡛࠶ࡿ㸬༳࡛♧ࡋࡓึᮇ఩⨨࡟ᑐࡋ࡚㸪㛗᪉ᙧ✵㛫ࡢ㛗ᡭ᪉ྥ(x ㍈᪉ྥ)࡟࠾஫࠸࠿ࡽ㐲ࡊ࠿ࡿࡼ࠺࡟⛣ືࡋ࡚࠸ࡿࡇ࡜ࡀศ࠿ࡿ㸬୍᪉ y ㍈᪉ྥ࡟ࡣྠࡌ
఩⨨ࢆಖࡗ࡚࠸ࡿ㸬ࡇࢀࡣ[㸰]ࡢ◊✲࡛♧ࡉࢀࡓ⤖ᯝ࡟୍⮴ࡍࡿ㸬

ᅗ2 ࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝ

4. ௒ᚋࡢᒎᮃᮏ◊✲࡛ࡣ㸪2 ḟඖࡢ✵㛫ⓗ➇தࣔࢹࣝࢆ࢚࣮ࢪ࢙ࣥࢺࣔࢹࣝ࡟ᣑᙇࡋ㸪࣐ࣝࢳ࢚࣮ࢪ࢙ࣥࢺࢩ࣑࣮ࣗࣞࢩࣙࣥࢆᵓ⠏ࡋࡓ㸬௒ᚋࡣ㸪ᵓ⠏ࡋࡓࢩ࣑࣮ࣗࣞࢱࢆ⏝࠸࡚㸪ᚑ᮶ࡢゎᯒⓗ࡞࢔ࣉ࣮ࣟࢳ࡛ࡣゎࡃࡇ࡜ࡢ࡛ࡁ࡞࠿ࡗࡓ」㞧࡞≧ἣࢆࣔࢹࣝ࡟⤌ࡳ㎸ࡳ㸪ᵝࠎ࡞≧ἣ࡟࠾ࡅࡿ✵㛫ⓗ➇த࡟ࡘ࠸࡚ㄪ࡭࡚࠸ࡃࡇ࡜ࢆ┠ᣦࡍ㸬౛࠼ࡤ㸪ᾘ㈝⪅ࡢศᕸࡀ୍ᵝ࡛࡞࠿ࡗࡓࡾ㸪᫬㛫ኚ໬ࡋࡓࡾࡍࡿሙྜ㸪ᾘ㈝⪅࡟ࡼࡿ௻ᴗ㑅ᢥࡢࣔࢹࣝࡀከᵝ࡞ሙྜ㸪ᕷሙ✵㛫࡟࠾ࡅࡿ௻ᴗࡢ⛣ື⠊ᅖࡀఱࡽ࠿ࡢせᅉ࡛ไ㝈ࡉࢀࡿሙྜ࡞࡝ࡀ⪃࠼ࡽࢀࡿ㸬ཧ⪃ᩥ⊩[㸯] Hotelling H.: Stability in Competition, Economic Journal,
Vol. 39, No. 153, pp. 41-57, (1929)[㸰] TabuchiT.:Two-stage

Two-dimensional

SpatialCompetition between Two Firms, Regional Science andUrban Economics, Vol. 24, No. 2, pp. 207-227, (1994)[㸱] Aumann R. J. : Backward Induction and Common
Knowledge of Rationality, Games and Economic Behavior
Vol. 8 No. 1, pp. 6-19, (1995)

ᅗ1 ࢩ࣑࣮ࣗࣞࢩࣙࣥࡢὶࢀ