The Complexity Analysis for Price Game Model of Risk-Averse Supply Chain Considering Fairness Concern

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/9216193/figures/9216193.fig.008a.svgz" name="9216193.fig.008a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>The plane of <svg height="11.8174pt" id="M148" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 13.1624 11.8174" width="13.1624pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg> and <svg height="11.8174pt" id="M149" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 13.1624 11.8174" width="13.1624pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg> with <svg height="11.6399pt" id="M150" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -8.34882 55.0836 11.6399" width="55.0836pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.059,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.637,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.9,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.14,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.104,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,42.344,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,48.584,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z"></path></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/9216193/figures/9216193.fig.008b.svgz" name="9216193.fig.008b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>The plane of <svg height="12.4698pt" id="M151" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 12.8362 12.4698" width="12.8362pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg> and <svg height="12.4698pt" id="M152" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 12.8362 12.4698" width="12.8362pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg> with <svg height="11.6399pt" id="M153" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -8.34882 55.0836 11.6399" width="55.0836pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.059,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.637,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.9,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.14,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.104,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,42.344,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,48.584,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z"></path></g></svg></td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/complexity/volume-2018/9216193/figures/9216193.fig.008c.svgz" name="9216193.fig.008c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>The plane of <svg height="11.8174pt" id="M154" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 13.1624 11.8174" width="13.1624pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg> and <svg height="11.8174pt" id="M155" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 13.1624 11.8174" width="13.1624pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg> with <svg height="11.6399pt" id="M156" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -8.34882 55.0836 11.6399" width="55.0836pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.059,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.637,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.9,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.14,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.104,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 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class="fig-caption"><td><b>(d) </b>The plane of <svg height="12.4698pt" id="M157" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 12.8362 12.4698" width="12.8362pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg> and <svg height="12.4698pt" id="M158" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 12.8362 12.4698" width="12.8362pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg> with <svg height="11.6399pt" id="M159" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -8.34882 55.0836 11.6399" width="55.0836pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.059,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.637,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.9,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.14,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.104,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,42.344,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,48.584,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g></svg></td></tr></table>

<div>The 2D bifurcation diagram of system (<a href="https://static.hindawi.com/articles/complexity/volume-2018/9216193/figures/#EEq3">12</a>).</div>

Complexity

fig8

Figure 8

Figure 8: The Complexity Analysis for Price Game Model of Risk-Averse Supply Chain Considering Fairness Concern 